English

Fatou's Lemma for Weakly Converging Probabilities

Probability 2013-11-25 v3

Abstract

Fatou's lemma states under appropriate conditions that the integral of the lower limit of a sequence of functions is not greater than the lower limit of the integrals. This note describes similar inequalities when, instead of a single measure, the functions are integrated with respect to different measures that form a weakly convergent sequence.

Keywords

Cite

@article{arxiv.1206.4073,
  title  = {Fatou's Lemma for Weakly Converging Probabilities},
  author = {Eugene A. Feinberg and Pavlo O. Kasyanov and Nina V. Zadoianchuk},
  journal= {arXiv preprint arXiv:1206.4073},
  year   = {2013}
}
R2 v1 2026-06-21T21:21:35.879Z