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Topics referred to by the same term
Look up hyperfinite in Wiktionary, the free dictionary. Hyperfinite may refer to: Hyperfinite set, a type of internal set in non-standard analysis Hyperfinite
Hyperfinite
Type of internal set in nonstandard analysis
Hyperfinite sets share the properties of finite sets: A hyperfinite set has minimal and maximal elements, and a hyperfinite union of a hyperfinite collection
Hyperfinite_set
*-algebra of bounded operators on a Hilbert space
are the hyperfinite type II1 factor and the hyperfinite type II∞ factor, found by Murray & von Neumann (1936). These are the unique hyperfinite factors
Von_Neumann_algebra
Swiss mathematician (1707–1783)
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Leonhard_Euler
In descriptive set theory and related areas of mathematics, a hyperfinite equivalence relation on a standard Borel space X is a Borel equivalence relation
Hyperfinite equivalence relation
Hyperfinite_equivalence_relation
Unique von Neumann algebra
mathematics, there are up to isomorphism exactly two separably acting hyperfinite type II factors; one infinite and one finite. Murray and von Neumann
Hyperfinite_type_II_factor
Calculus using a logically rigorous notion of infinitesimal numbers
and Robinson show that if T is polynomially compact, then there is a hyperfinite index w such that the matrix coefficient aw+1,w is infinitesimal. Next
Nonstandard_analysis
Branch of mathematics
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Calculus
C*-algebra
counterpart of simple AF C*-algebras in the von Neumann algebra world are the hyperfinite factors, which were classified by Connes and Haagerup. In the context
Approximately finite-dimensional C*-algebra
Approximately_finite-dimensional_C*-algebra
Modern application of infinitesimals
f(x_{i})} for all i = 0, …, N (an alternative explanation is that every hyperfinite set admits a maximum). Consider the real point c = s t ( x i 0 ) {\displaystyle
Nonstandard_calculus
mathematics, particularly in the theory of C*-algebras, a uniformly hyperfinite, or UHF, algebra is a C*-algebra that can be written as the closure,
Uniformly_hyperfinite_algebra
French mathematician and lawyer (1601–1665)
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Pierre_de_Fermat
In mathematics, a hyper-finite field is an uncountable field similar in many ways to finite fields. More precisely a field F is called hyper-finite if
Hyper-finite_field
Hungarian and American mathematician and physicist (1903–1957)
continuous geometry other than projective space was the projections of the hyperfinite type II factor. In more pure lattice theoretical work, he solved the
John_von_Neumann
Generalization of the real numbers
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Surreal_number
Mathematical symbol used to denote integrals and antiderivatives
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Integral_symbol
Mathematical notation used for calculus
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Leibniz's_notation
Extremely small quantity in calculus; thing so small that there is no way to measure it
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Infinitesimal
French mathematician (1789–1857)
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Augustin-Louis_Cauchy
German polymath (1646–1716)
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Gottfried_Wilhelm_Leibniz
Mathematical concept for comparing objects
Property of segments that have the same length and the same direction Hyperfinite equivalence relation Quotient by an equivalence relation – Generalization
Equivalence_relation
Mathematics award
theorem of factors of type III, classification of automorphisms of the hyperfinite factor, classification of injective factors, and applications of the
Fields_Medal
Mathematical term
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Microcontinuity
New Zealand mathematician and Fields Medalist
of Geneva in 1979. His thesis, titled Actions of finite groups on the hyperfinite II1 factor, was written under the supervision of André Haefliger, and
Vaughan_Jones
Real numbers adjoined with a nil-squaring element
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Dual_number
Locally compact topological group with an invariant averaging operation
is hyperfinite (A. Connes). Note that A. Connes also proved that the von Neumann group algebra of any connected locally compact group is hyperfinite, so
Amenable_group
Function from the limited hyperreal to the real numbers
{\displaystyle \Delta x} is taken to be infinitesimal, exploiting a hyperfinite partition of the interval [a,b]. Given a sequence ( u n ) {\displaystyle
Standard_part_function
Calculus textbook by Guillaume de l'Hôpital (1696)
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Analyse des infiniment petits pour l'intelligence des lignes courbes
Analyse_des_infiniment_petits_pour_l'intelligence_des_lignes_courbes
Element of a nonstandard model of the reals, which can be infinite or infinitesimal
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Hyperreal_number
Mathematical problem in von Neumann algebra theory
\omega } be a free ultrafilter on the natural numbers and let R be the hyperfinite type II1 factor with trace τ {\displaystyle \tau } . One can construct
Connes_embedding_problem
continuous geometry other than projective space was the projections of the hyperfinite type II factor. Menger and Birkhoff gave axioms for projective geometry
Continuous_geometry
Application of Fourier analysis to non-abelian topological groups
infinite symmetric group, where the von Neumann group algebra is the hyperfinite type II1 factor. The further theory divides up the Plancherel measure
Noncommutative harmonic analysis
Noncommutative_harmonic_analysis
Concept in mathematics
is Fermion Walsh system in non-commutative Lp spaces associated with hyperfinite type II factor. The Fermion Walsh system is a non-commutative, or "quantum"
Walsh_function
Topics referred to by the same term
acidemia type 2 Glycogen storage disease type II Hyper-IgM syndrome type 2 Hyperfinite type II factor Type 2 connector, used for charging electric vehicles
Type_2
absolutely irreducible variety over F has a point defined over F). Every hyperfinite field is pseudo-finite and every pseudo-finite field is quasifinite.
Pseudo-finite_field
Topological algebra associated to continuous groups
consists only of complex multiples of the identity. NG is isomorphic to the hyperfinite type II1 factor if and only if G is countable, amenable, and has the
Group algebra of a locally compact group
Group_algebra_of_a_locally_compact_group
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Criticism of nonstandard analysis
Criticism_of_nonstandard_analysis
Named set of points in nonstandard analysis
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Monad_(nonstandard_analysis)
Geometrical concept relating area and volume
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Cavalieri's_principle
Mathematical treatise by Archimedes
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
The Method of Mechanical Theorems
The_Method_of_Mechanical_Theorems
Textbook by Augustin-Louis Cauchy (1821)
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Cours_d'analyse
of hyperfinite Type III factors. From this classification and results in ergodic theory, it is known that every infinite-dimensional hyperfinite factor
Crossed_product
System of mathematical set theory
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Internal_set_theory
Mathematical notion of infinitesimal difference
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Differential_(mathematics)
Girard, Jean-Yves (2011). "Geometry of interaction V: logic in the hyperfinite factor". Theoretical Computer Science. 412 (20): 1860–1883. Seiller,
Geometry_of_interaction
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Increment_theorem
Formalization in mathematical topos theory
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Synthetic differential geometry
Synthetic_differential_geometry
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Constructive nonstandard analysis
Constructive_nonstandard_analysis
Descriptive set theory relation
concept encapsulates various more specific concepts, such as that of a hyperfinite equivalence relation, but is of interest in and of itself. A main area
Countable_Borel_relation
American mathematician
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Abraham_Robinson
Generalized natural number
Supernatural numbers also arise in the classification of uniformly hyperfinite algebras. Profinite integer Steinitz, Ernst (1910). "Algebraische Theorie
Supernatural_number
two standard Borel spaces X and Y are Borel-isomorphic iff |X| = |Y|. Hyperfinite equivalence relation Wadge hierarchy Entourage (topology) – Topological
Borel_equivalence_relation
Principle that whatever succeeds for the finite also succeeds for the infinite
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Law_of_continuity
Mathematical model for describing material deformation under stress
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Infinitesimal_strain_theory
Heuristic principle enunciated by Gottfried Wilhelm Leibniz
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Transcendental law of homogeneity
Transcendental_law_of_homogeneity
1734 book by George Berkeley
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
The_Analyst
Concept in model theory
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Transfer_principle
Mathematical procedure equivalent to differential calculus
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Adequality
American physicist
H.; Hastings, Matthew B. (January 2014). "Quantum Systems on Non-$k$-Hyperfinite Complexes: a generalization of classical statistical mechanics on expander
Matthew_Hastings
System of numbers with non-finite quantities
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Levi-Civita_field
decompositions. In this case if M {\displaystyle M} and N {\displaystyle N} are hyperfinite, Sorin Popa showed that the inclusion N ⊂ M {\displaystyle N\subset M}
Subfactor
Partially unsolved problem in mathematics
original idea of embedding the infinite-dimensional Hilbert space in a hyperfinite-dimensional Hilbert space (see Non-standard analysis#Invariant subspace
Invariant_subspace_problem
Type of set in mathematical logic
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Internal_set
together with Loeb measure theory allows one to define Brownian motion as a hyperfinite random walk, obviating the need for cumbersome measure-theoretic developments
Influence of nonstandard analysis
Influence_of_nonstandard_analysis
Proof technique in nonstandard analysis
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Overspill
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Glossary_of_calculus
American mathematician (1934–2011)
which culminated in work by Alain Connes relating injectivity to hyperfiniteness. One of the major features of Arveson's work was the use of algebras
William_Arveson
Lie group of complex numbers of unit modulus; topologically a circle
non-standard analysis, the most natural replacement of the circle group is the hyperfinite cyclic group C N = ∗ Z / N ∗ Z , {\displaystyle C_{N}={}^{*}\mathbb {Z}
Circle_group
Indian-American statistician
master's degree in 1994 with a thesis supervised by Stephen Durham on hyperfinite probability theory and completed her Ph.D. in 1996. Her doctoral advisor
Nairanjana_Dasgupta
2 *-anti-automorphism of a von Neumann factor of the same type. For hyperfinite factors, the class of von Neumann factors completely classified by Connes
Jordan_operator_algebra
Ordered field that does not satisfy the Archimedean property
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Non-Archimedean_ordered_field
American mathematician
Society. His most famous paper is called "On Constructing Non -*Isomorphic Hyperfinite Factors of Type III" He also wrote the book " An XT Called Stanley" Under
Robert_T._Powers
1976 mathematics textbook by H. Jerome Keisler
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Elementary Calculus: An Infinitesimal Approach
Elementary_Calculus:_An_Infinitesimal_Approach
American mathematician (born 1947)
Papers, 1980 'Notes on *finite cooperative games', RAND Papers, 1981 'Hyperfinite Von Neumann games', Mathematical Social Sciences, Vol. 9, No. 2 (1985)
Alain_A._Lewis
Quantum computational theorem on problem complexity
H.; Hastings, Matthew B. (January 2014). "Quantum Systems on Non-$k$-Hyperfinite Complexes: a generalization of classical statistical mechanics on expander
NLTS_conjecture
A finite depth hyperfinite subfactor is amenable. About the non-amenable case: there are unclassifiably many irreducible hyperfinite subfactors of index
Planar_algebra
Hyperreal number that is equal to its own integer part
Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of
Hyperinteger
HYPERFINITE
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HYPERFINITE
Surname or Lastname
English
English : variant spelling of the habitational name Aughton, from any of three places, in Lancashire, East and South Yorkshire, named Aughton, from Old English as Äc ‘oak’ + tÅ«n ‘settlement’.Possibly French : there are several places in France named Authon and it could be a habitational name from any of these.
Boy/Male
Tamil
Lotus
Girl/Female
Gaelic Irish
Oath.
Boy/Male
Muslim
The guide, The way
Boy/Male
Indian
Ethical heart, Moral soul
Boy/Male
Hindu
Shiva
Male
Irish
Variant spelling of Irish Gaelic Ailill, OILILL means "elf."
Girl/Female
Tamil
Nishhcitha | நீஷà¯à®šà¯€à®Ÿà®¾Â
Girl/Female
Arabic, Muslim
Paradise
Boy/Male
Teutonic
Strong as an eagle.
HYPERFINITE
HYPERFINITE
HYPERFINITE
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