Uniform Integrability - Relevant Theorems

Relevant Theorems

  • Dunford–Pettis theorem
A class of random variables is uniformly integrable if and only if it is relatively compact for the weak topology.
  • de la VallĂ©e-Poussin theorem
The family is uniformly integrable if and only if there exists a non-negative increasing convex function such that
and

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