Fatou’s lemma for weakly converging probabilities

E. A. Feinberg; P. O. Kasyanov; N. V. Zadoianchuk

doi:10.1137/S0040585X97986850

Fatou’s lemma for weakly converging probabilities

E. A. Feinberg
, P. O. Kasyanov
, N. V. Zadoianchuk

Applied Mathematics and Statistics

National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"

Research output: Contribution to journal › Article › peer-review

42 Scopus citations

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 paper describes similar inequalities when, instead of a single measure, the functions are integrated with respect to different measures that form a weakly convergent sequence.

Original language	English
Pages (from-to)	683-689
Number of pages	7
Journal	Theory of Probability and its Applications
Volume	58
Issue number	4
DOIs	https://doi.org/10.1137/S0040585X97986850
State	Published - 2014

Keywords

Fatou lemma
Measure
Probability
Weak convergence

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title = "Fatou{\textquoteright}s lemma for weakly converging probabilities",

abstract = "Fatou{\textquoteright}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 paper 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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AU - Feinberg, E. A.

AU - Kasyanov, P. O.

AU - Zadoianchuk, N. V.

PY - 2014

Y1 - 2014

N2 - 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 paper describes similar inequalities when, instead of a single measure, the functions are integrated with respect to different measures that form a weakly convergent sequence.

AB - 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 paper describes similar inequalities when, instead of a single measure, the functions are integrated with respect to different measures that form a weakly convergent sequence.

KW - Fatou lemma

KW - Measure

KW - Probability

KW - Weak convergence

UR - https://www.scopus.com/pages/publications/84919627894

U2 - 10.1137/S0040585X97986850

DO - 10.1137/S0040585X97986850

M3 - Article

AN - SCOPUS:84919627894

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VL - 58

SP - 683

EP - 689

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

IS - 4

ER -

Fatou’s lemma for weakly converging probabilities

Abstract

Keywords

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