Home›Probability and Statistics›Statement Form›CharacterizationConceptCharacterizationLogic, Foundations and Set TheoryReference and ClassificationDevelopingIn mathematics, a characterization of an object is a set of conditions that, while possibly different from the definition of the object, is logically equivalent to it. The cited article explains that to say a property characterizes an object is to say that not only does the object have the property, but that it is the only thing that has it, and that even though a characterization identifies an object uniquely, several characterizations can exist for a single object. It notes the common phrasings that a property is necessary and sufficient for the object, or that the object holds if and only if the property does. Theorems stated as if and only if conditions are grouped under this concept.CharacterizationConnectionsSourcesTake a Related QuizComments (0)Reader Challenges (0)CharacterizationFilter Results22 entriesBranchAllMeasure Theory (1)Probability and Statistics (20)Topic AreaAllLearning, Inference and Decision Under Uncertainty (1)Mathematical Statistics and Estimation (8)Probability Theory (9)Stochastic Processes and Martingales (3)ProvedAll1713 (1)1929 (1)1930 (1)1933 (2)1934 (1)1938 (1)1943 (1)1951 (1)1952 (1)1955 (1)1963 (1)2000 (1)2019 (1)Proved ByAllAbraham Wald (1)Andrey Kolmogorov (1)Carl Friedrich Gauss (1)David Blackwell (1)Edwin Hewitt (1)Francesco Paolo Cantelli (1)George Udny Yule (1)Harald Cramér (1)Jacob Bernoulli (3)Paul Lévy (1)Ronald Fisher (1)William Gemmell Cochran (1)Show ResultsBrowseCompareSelect all 22Basu's TheoremCharacterizationChung-Fuchs TheoremCharacterizationCochran's TheoremCharacterizationContinuous Mapping TheoremCharacterizationde Finetti's TheoremCharacterizationDelta MethodCharacterizationDonsker's TheoremCharacterizationFalse Confidence TheoremCharacterizationFisher-Neyman Factorization TheoremCharacterizationFrisch-Waugh-Lovell TheoremCharacterizationGauss-Markov TheoremCharacterizationGlivenko-Cantelli TheoremCharacterizationHewitt-Savage Zero-One LawCharacterizationLaw of Large NumbersCharacterizationLevy's Continuity TheoremCharacterizationRabin's Calibration TheoremCharacterizationRao-Blackwell TheoremCharacterizationSlutsky's TheoremCharacterizationStrong Law of Large NumbersCharacterizationStructure Theorem for Gaussian MeasuresCharacterizationWeak Law of Large NumbersCharacterizationWilks' TheoremCharacterizationConnectionsIn BranchLogic and Foundations, Branches of Mathematics Well-attested Source Wolfram MathWorld: CharacterizationStatement Form OfMazur's Control Theorem, Theorems Well-attested Miquel's Theorem, Theorems Well-attested Modigliani-Miller Theorem, Theorems Well-attested Modularity Theorem, Theorems Well-attested Mohr-Mascheroni Theorem, Theorems Well-attested Monge's Theorem, Theorems Well-attested Monotone Convergence Theorem, Theorems Well-attested Montel's Theorem, Theorems Well-attested Mordell-Weil Theorem, Theorems Well-attested Morera's Theorem, Theorems Well-attested Morley's Categoricity Theorem, Theorems Well-attested Morley's Trisector Theorem, Theorems Well-attested Moving Equilibrium Theorem, Theorems Well-attested Muntz-Szasz Theorem, Theorems Well-attested Myhill Isomorphism Theorem, Theorems Well-attested Myhill-Nerode Theorem, Theorems Well-attested Nagata-Smirnov Metrization Theorem, Theorems Well-attested Nagell-Lutz Theorem, Theorems Well-attested Namioka's Theorem, Theorems Well-attested Napoleon's Theorem, Theorems Well-attested Nash-Williams Formula, Theorems Well-attested Nernst's Theorem, Theorems Well-attested Nielsen-Schreier Theorem, Theorems Well-attested Noether's Isomorphism Theorems, Theorems Well-attested No-Hair Theorem, Theorems Well-attested Odd Number Theorem, Theorems Well-attested Okishio's Theorem, Theorems Well-attested Open Mapping Theorem (Complex Analysis), Theorems Well-attested Open Mapping Theorem (Functional Analysis), Theorems Well-attested Pascal's Theorem, Theorems Well-attested Perfect Graph Theorem, Theorems Well-attested Peter-Weyl Theorem, Theorems Well-attested Phragmen-Lindelof Principle, Theorems Well-attested Poincare Conjecture, Theorems Well-attested Poincare Duality Theorem, Theorems Well-attested Poincare-Birkhoff-Witt Theorem, Theorems Well-attested Poncelet-Steiner Theorem, Theorems Well-attested Post's Theorem, Theorems Well-attested Principal Ideal Theorem, Theorems Well-attested Proof That e Is Irrational, Theorems Well-attested Proof that Pi is Irrational, Theorems Well-attested Rabin's Calibration Theorem, Theorems Well-attested Rademacher's Theorem, Theorems Well-attested Rao-Blackwell Theorem, Theorems Well-attested Rational Root Theorem, Theorems Well-attested Reeh-Schlieder Theorem, Theorems Well-attested Reflection Theorem, Theorems Well-attested Reidemeister's Theorem, Theorems Well-attested Revelation Principle, Theorems Well-attested Rice-Shapiro Theorem, Theorems Well-attested Showing 151 to 200 of 262 in Statement Form Of, page 4 of 6.← Previous123456Next →SourcesCharacterizationWikipedia, lead sectionQuote, Wikipedia, lead sectionIn mathematics, a characterization of an object is a set of conditions that, while possibly different from the definition of the object, is logically equivalent to it.View the SourceWolfram MathWorld: CharacterizationWolfram MathWorldIn Branch: Logic and Foundations, Subject classificationsQuote, In Branch: Logic and Foundations, Subject classificationsFoundations of Mathematics Theorem ProvingView the SourceTake a Related QuizOrigins of Mathematical ConceptsCovers this kind of entry.Comments (0)No comments yet. 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