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 Of15 and 290 Theorems, Theorems Well-attested Abel's Test, Theorems Well-attested Adiabatic Theorem, Theorems Well-attested Ado's Theorem, Theorems Well-attested AM-GM Inequality, Theorems Well-attested Apery's Theorem, Theorems Well-attested Arzela-Ascoli Theorem, Theorems Well-attested Ax-Grothendieck Theorem, Theorems Well-attested Baire Category Theorem, Theorems Well-attested Banach-Alaoglu Theorem, Theorems Well-attested Banach-Steinhaus Theorem, Theorems Well-attested Barwise Compactness Theorem, Theorems Well-attested Basu's Theorem, Theorems Well-attested Beckman-Quarles Theorem, Theorems Well-attested Berge's Theorem, Theorems Well-attested Bernstein's Theorem on Monotone Functions, Theorems Well-attested Birch's Theorem, Theorems Well-attested Birkhoff's Theorem (Electromagnetism), Theorems Well-attested Birkhoff's Theorem (General Relativity), Theorems Well-attested Blackwell's Informativeness Theorem, Theorems Well-attested Bochner's Theorem, Theorems Well-attested Bondareva-Shapley Theorem, Theorems Well-attested Bondy-Chvatal Theorem, Theorems Well-attested Brauer-Siegel Theorem, Theorems Well-attested Brianchon's Theorem, Theorems Well-attested Brown Representability Theorem, Theorems Well-attested Burnside's Theorem, Theorems Well-attested Cartan-Hadamard Theorem, Theorems Well-attested Casorati-Weierstrass Theorem, Theorems Well-attested Cayley-Bacharach Theorem, Theorems Well-attested Cayley's Theorem, Theorems Well-attested Ceva's Theorem, Theorems Well-attested Chowla-Mordell Theorem, Theorems Well-attested Chow's Theorem, Theorems Well-attested Chung-Fuchs Theorem, Theorems Well-attested Clifford's Circle Theorems, Theorems Well-attested Closed Graph Theorem, Theorems Well-attested Coase Theorem, Theorems Well-attested Cochran's Theorem, Theorems Well-attested Commutator Subgroup, Theorems Well-attested Compactness Theorem, Theorems Well-attested Complex Conjugate Root Theorem, Theorems Well-attested Constructibility of the Regular Heptadecagon, Theorems Well-attested Continuous Mapping Theorem, Theorems Well-attested Cook-Levin Theorem, Theorems Well-attested Courcelle's Theorem, Theorems Well-attested CPT Theorem, Theorems Well-attested Crystallographic Restriction Theorem, Theorems Well-attested Curtis-Hedlund-Lyndon Theorem, Theorems Well-attested Davenport-Schmidt Theorem, Theorems Well-attested Showing 1 to 50 of 262 in Statement Form Of, page 1 of 6.123…6Next →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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