Linked from

The 12 pages that link to Uniform integrability, each with the reason it gives.

• IntegralRelated: It helps determine when convergence of functions also yields convergence of integrals.

• Convergence in probabilityRelated: Together with probability convergence, it can yield convergence in mean.

• Dominated convergence theoremCompared with: Uniform integrability can replace a single pointwise integrable bound in convergence results.

• Weak convergenceRelated: It helps ensure weak convergence of functions also controls convergence of integrals.

• Integrable functionCompared with: It strengthens individual integrability into a uniform condition across a family.

• Optional stopping theoremRelated: It supplies a powerful condition under which stopped martingales retain their expectations.

• Prokhorov's theoremCompared with: It controls large values in probability theory, whereas tightness controls where probability mass lies.

• Continuous mapping theoremRelated: It supplies extra control when transformed limits involve expectations rather than distributions.

• Doob martingaleRelated: It supplies conditions under which a convergent martingale also converges in mean.

• Fatou's lemmaRelated: Uniform integrability can supply the extra control needed for convergence beyond Fatou's bound.

• Wald's equationRelated: It can supply conditions for passing expectations through limits of stopped partial sums.

• Doob's martingale inequalityRelated: Doob's maximal inequality helps transfer uniform integrability from terminal values to process maxima.