Uniform Integrability
Uniform integrability controls the contribution of large values across a family of random variables. It supplies the extra condition that upgrades convergence in probability to convergence in mean.
Before opening the references
expectation · convergence in probability · Lp convergence of random variables
Where to read
Start here: Probability: Theory and Examples (Version 5)
Rick Durrett · Book · English · Free full text
§4.6 Uniform Integrability, opening definition and Theorem 4.6.3 (convergence in probability plus uniform integrability versus L1 convergence)
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Probability Theory in the library · Preparation and skip guidance