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arxiv: 1206.4073 · v3 · pith:OIWPGT7Ynew · submitted 2012-06-18 · 🧮 math.PR

Fatou's Lemma for Weakly Converging Probabilities

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keywords fatoufunctionslemmalimitlowersequenceweaklyappropriate
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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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