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 OfDe Bruijn-Erdos Theorem (Graph Theory), Theorems Well-attested de Finetti's Theorem, Theorems Well-attested De Rham's Theorem, Theorems Well-attested Deduction Theorem, Theorems Well-attested Delta Method, Theorems Well-attested Desargues' Theorem, Theorems Well-attested Diaconescu's Theorem, Theorems Well-attested Dini's Theorem, Theorems Well-attested Discontinuities of Monotone Functions, Theorems Well-attested Donsker's Theorem, Theorems Well-attested Edgeworth's Limit Theorem, Theorems Well-attested Ehrenfeucht-Fraisse Theorem, Theorems Well-attested Equal Incircles Theorem, Theorems Well-attested Equidistribution Theorem, Theorems Well-attested Erdos-Gallai Theorem, Theorems Well-attested Euclid-Euler Theorem, Theorems Well-attested Ewald-Oseen Extinction Theorem, Theorems Well-attested Factor Price Equalization, Theorems Well-attested False Confidence Theorem, Theorems Well-attested Feit-Thompson Theorem, Theorems Well-attested Fermat's Theorem on Sums of Two Squares, Theorems Well-attested Fisher Separation Theorem, Theorems Well-attested Fisher-Neyman Factorization Theorem, Theorems Well-attested Free Will Theorem, Theorems Well-attested Frege's Theorem, Theorems Well-attested Freiman's Theorem, Theorems Well-attested Frisch-Waugh-Lovell Theorem, Theorems Well-attested Fubini's Theorem on Differentiation, Theorems Well-attested Fundamental Theorem of Equivalence Relations, Theorems Well-attested Fundamental Theorem of Topos Theory, Theorems Well-attested Fundamental Theorems of Welfare Economics, Theorems Well-attested Furstenberg's Proof of the Infinitude of Primes, Theorems Well-attested Gamas's Theorem, Theorems Well-attested Gauss-Lucas Theorem, Theorems Well-attested Gauss-Markov Theorem, Theorems Well-attested Gauss's Lemma (Polynomials), Theorems Well-attested Gauss's Theorema Egregium, Theorems Well-attested Gelfond-Schneider Theorem, Theorems Well-attested Gleason's Theorem, Theorems Well-attested Glivenko-Cantelli Theorem, Theorems Well-attested Going-Up and Going-Down Theorems, Theorems Well-attested Goursat's Theorem, Theorems Well-attested Graph Structure Theorem, Theorems Well-attested Grinberg's Theorem, Theorems Well-attested Hasse Norm Theorem, Theorems Well-attested Hasse-Minkowski Theorem, Theorems Well-attested Heckscher-Ohlin Theorem, Theorems Well-attested Heine-Borel Theorem, Theorems Well-attested Henry George Theorem, Theorems Well-attested Herbrand-Ribet Theorem, Theorems Well-attested Showing 51 to 100 of 262 in Statement Form Of, page 2 of 6.← Previous1234…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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