User:Caliburn/roadmap
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Probability
Conditional Expectation
Definition:Conditional Expectation/General CaseExistence and Essential Uniqueness of Conditional Expectation Conditioned on Sigma-Algebra- Conditional Expectation on Countably Generated Sigma-Algebra
- Conditional Monotone Convergence Theorem
- Conditional Dominated Convergence Theorem
- Expectation of Conditional Expectation
- Conditional Expectation of Measurable Random Variable
- Conditional Expectation of Non-Negative Random Variable is Non-Negative
- Conditional Expectation is Linear
- Triangle Inequality for Conditional Expectation
- Conditional Fatou's Lemma
- Conditional Jensen's Inequality
- Conditional Expectation with respect to Independent Sigma-Algebras
Analysis
Distributions
- Pointwise Limit of Distributions is Distribution - uses Banach-Steinhaus
- Derivative of Schwartz Function is Schwartz Function
- Product of Schwartz Functions is Schwartz Function
- Schwartz Function is Subset of Lebesgue p-Space
- Fourier Transform of Schwartz Function is Schwartz Function
- Fourier Transform of Convolution
- Inverse Fourier Transform is Inverse of Fourier Transform
- Plancherel's Formula
- Derivative of Tempered Distribution is Tempered Distribution
- Product of Schwartz Function and Tempered Distribution is Tempered Distribution
- Fourier Transform of Tempered Distribution is Self-Adjoint
- Limit of Fourier Transform of Convergent Sequence of Tempered Distributions is Fourier Transform of Limit