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 f n that converges to f in distribution, there exists a sequence of automorphisms S n of ([0, 1], µ) such that f n(S n(t)) converges to f(t) in measure. Connection with some known results is also discussed.
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References
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Original Russian Text © F. A. Talalyan, 2016, published in Izvestiya Natsional’noi Akademii Nauk Armenii, Matematika, 2016, No. 5, pp. 74-80.
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Talalyan, F.A. On the metric type of measurable functions and convergence in distribution. J. Contemp. Mathemat. Anal. 51, 227–231 (2016). https://doi.org/10.3103/S1068362316050034
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DOI: https://doi.org/10.3103/S1068362316050034