Conditional expectation given a sigma algebra

Depends on

• Expectation of a nonnegative or integrable random variable
• The class $L^1(\mu)$ of integrable functions

Used by

• Conditional flow matching for inverse posteriors Algorithm
• Conditional flow-matching training and exact-flow sampling Algorithm
• Invariant conditional-entropy description of the SMB limit Corollary
• A supermartingale supremum threshold need not be attained Counterexample
• An L1-bounded martingale need not converge in L1 Counterexample
• Marginal sub-Gaussianity does not justify an anytime confidence sequence Counterexample
• Bandit importance-weighted estimator Definition
• Conditional expectation as an ae class Definition
• Conditional independence given a sigma-algebra Definition
• Conditional tests given a statistic Definition
• Conditionally sub-Gaussian increments Definition
• Finite-dimensional linear contextual bandit model Definition
• Minimal sufficient sigma-fields Definition
• Probability calibration and calibration error Definition
• Regular conditional distribution Definition
• Two-stage randomized design and strategy-specific effects Definition
• A finite-history conditional mean can be nonlinear Example
• A noncommuting two-noise equation requires an area term Example
• A predictable linear forecast and its empirical residual process Example
• Gambler’s ruin from harmonicity Example
• Noisy simulator output separates intrinsic noise from input variance Example
• A finite label has a conditional probability function Lemma
• A policy score has zero conditional mean before the action Lemma
• A state-dependent action-independent baseline preserves the gradient mean Lemma
• Conditional expectation is unique almost surely Lemma
• Conditional expectation on positive-probability events in finite spaces Lemma
• Conditional flow-matching batch gradients and exact-flow output law Lemma
• Conditional independence under kernel extension and conditioning Lemma
• Conditional local defect bounds for the Milstein Taylor increment Lemma
• Conditional moments of the bandit importance-weighted estimator Lemma
• Conditional sub-Gaussian bounds allow bounded predictable coefficients Lemma
• Conditional-independence factorization for integrable outcomes Lemma
• Conditioning a known state and independent noise Lemma
• Exp4 expert reward estimates are conditionally unbiased Lemma
• Exp4 weighted estimated loss has conditional second moment at most k Lemma
• Independent errors imply mediation cross-world independence Lemma
• Population regression and exact-flow meaning of conditional flow matching Lemma
• Product identity and conditional moments for iterated Brownian integrals Lemma
• The backdoor criterion implies conditional exchangeability Lemma
• The conditional Gaussian mixture is a nonnegative supermartingale Lemma

…and 38 more results.

Dependency tree · two levels

5 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

• Durrett, Probability: Theory and Examples, 5th ed. (standard reference, not scraped)