Fatou's Lemma for Weakly Converging Probabilities

Eugene A. Feinberg; Pavlo O. Kasyanov; Nina V. Zadoianchuk

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arXiv · 1206.4073

Fatou's Lemma for Weakly Converging Probabilities

Eugene A. Feinberg·Pavlo O. Kasyanov·Nina V. Zadoianchuk

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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.

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Eugene A. Feinberg, Pavlo O. Kasyanov, Nina V. Zadoianchuk. 2013-11-21. Fatou's Lemma for Weakly Converging Probabilities. https://arxiv.org/abs/1206.4073

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