Index
Glossary
Every definition, theorem, and lemma across my writing notes. Terms in the text link here.
Definitions
- 3 times an intervalDifferentiation
- AlgebraProduct Measures
- Borel-measurable functionFurther Foundations
- Characteristic FunctionCharacteristic Functions
- Conditional Probability and ExpectationConditional Probability and Expectation
- Convergence in probabilityInequalities and Convergence
- Cross sectionProduct Measures
- Cross sections of functionsProduct Measures
- Cumulative distribution functionDistributions
- Density functionDistributions
- DistributionDistributions
- Expected Value IExpected Values
- Expected Value IIExpected Values
- Finite measureProduct Measures
- Hardy-Littlewood Maximal FunctionDifferentiation
- IntegrationProduct Measures
- Kantorovich Dual ProblemKantorovich Duality
- Kantorovich Primal ProblemKantorovich Duality
- Markov ChainDiscrete Markov-Chains
- Monotone classProduct Measures
- n-th order transition probabilitiesDiscrete Markov-Chains
- Probability TripleProbability Triples
- Product of algebrasProduct Measures
- Product of measuresProduct Measures
- Random VariableFurther Foundations
- rectangleProduct Measures
- SemialgebraProbability Triples
- Simple random variableExpected Values
- Step functionApproximation by Step Functions
- Tail fieldFurther Foundations
- Tight distributionCharacteristic Functions
- VarianceExpected Values
- σ-finite measureProduct Measures
Theorems
- Borel-Cantelli LemmaFurther Foundations
- Central Limit TheoremCharacteristic Functions
- Change of Variable TheoremDistributions
- Continuity of ProbabilitiesFurther Foundations
- Continuity TheoremCharacteristic Functions
- Kolmogorov Zero-One LawFurther Foundations
- Lebesgue DecompositionDecomposition of Probability Laws
- Markov Chains ExistDiscrete Markov-Chains
- Monotone Class TheoremProduct Measures
- Radon-NikodymDecomposition of Probability Laws
- The Extension TheoremProbability Triples
- Weak Law of Large NumbersInequalities and Convergence
Lemmas
- Vitali Covering LemmaDifferentiation
Propositions
- A product of measures is a measureProduct Measures
- Approximation by continuous functionsApproximation by Step Functions
- Approximation by step functionsApproximation by Step Functions
- cross sections of measurable functions are measurableProduct Measures
- Cross sections preserve measurabilityProduct Measures
- Fourier InversionCharacteristic Functions
- Fourier Uniqueness TheoremCharacteristic Functions
- Fundamental Theorem of CalculusDifferentiation
- Hardy-Littlewood Maximal InequalityDifferentiation
- Helly Selection PrincipleCharacteristic Functions
- Lebesgue Differentiation Theorem v1Differentiation
- Measure of cross section is a measurable functionProduct Measures