Email this article On the metric type of measurable functions and convergence in distribution
- Authors: Talalyan F.A.1
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Affiliations:
- Institute ofMathematics
- Issue: Vol 51, No 5 (2016)
- Pages: 227-231
- Section: Functional Analysis
- URL: https://journal-vniispk.ru/1068-3623/article/view/227953
- DOI: https://doi.org/10.3103/S1068362316050034
- ID: 227953
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Abstract
In the present paper, sequences of real measurable functions defined on a measure space ([0, 1], µ), where µ is the Lebesgue measure, are studied. It is proved that for every sequence fn that converges to f in distribution, there exists a sequence of automorphisms Sn of ([0, 1], µ) such that fn(Sn(t)) converges to f(t) in measure. Connection with some known results is also discussed.
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About the authors
F. A. Talalyan
Institute ofMathematics
Author for correspondence.
Email: ftalalyan@mail.ru
Armenia, Yerevan
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