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Teoriya Veroyatnostei i ee Primeneniya, 2019, Volume 64, Issue 4, Pages 771–790
DOI: https://doi.org/10.4213/tvp5253
(Mi tvp5253)
 

This article is cited in 8 scientific papers (total in 8 papers)

Fatou's lemma for weakly converging measures under the uniform integrability condition

E. A. Feinberga, P. O. Kas'yanovb, Y. Lianga

a Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY, USA
b Institute for Applied System Analysis, National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute», Kyiv, Ukraine
Full-text PDF (574 kB) Citations (8)
References:
Abstract: This paper describes Fatou's lemma for a sequence of measures converging weakly to a finite measure and for a sequence of functions whose negative parts are uniformly integrable with respect to these measures. The paper also provides new formulations of uniform Fatou's lemma, uniform Lebesgue's convergence theorem, the Dunford–Pettis theorem, and the fundamental theorem for Young measures based on the equivalence of uniform integrability and the apparently weaker property of asymptotic uniform integrability for sequences of functions and finite measures.
Keywords: Fatou lemma, weak convergence of measures, uniform integrability, asymptotic uniform integrability.
Funding agency Grant number
National Science Foundation CMMI-1636193
The research of the first and third authors was supported by the NSF (grant CMMI-1636193).
Received: 09.10.2018
Revised: 18.03.2019
Accepted: 25.06.2019
English version:
Theory of Probability and its Applications, 2020, Volume 64, Issue 4, Pages 615–630
DOI: https://doi.org/10.1137/S0040585X97T989738
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: E. A. Feinberg, P. O. Kas'yanov, Y. Liang, “Fatou's lemma for weakly converging measures under the uniform integrability condition”, Teor. Veroyatnost. i Primenen., 64:4 (2019), 771–790; Theory Probab. Appl., 64:4 (2020), 615–630
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tvp5253
  • https://doi.org/10.4213/tvp5253
  • https://www.mathnet.ru/eng/tvp/v64/i4/p771
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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