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2021 Sufficient conditions for convergence of riemann sums for function space defined by the $k$-modulus of continuity
Igor E. Preobrazhenskii, P.G. Demidov
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Real Anal. Exchange 46(1): 37-50 (2021). DOI: 10.14321/realanalexch.46.1.0037

Abstract

For classes of functions defined by $k$-th moduli of continuity, calculated in the norm of the symmetric space $X$, an estimate of the difference of two members of the sequence of operators of Riemann sums on a set of large measure is given. The estimate is given in terms of a fundamental function of the space $X$. Using this result, for a function $f$ from a given symmetric space, sufficient conditions are given for the almost everywhere convergence of the sequence of operators of Riemann sums to the Lebesgue integral of a given function.

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Igor E. Preobrazhenskii. P.G. Demidov. "Sufficient conditions for convergence of riemann sums for function space defined by the $k$-modulus of continuity." Real Anal. Exchange 46 (1) 37 - 50, 2021. https://doi.org/10.14321/realanalexch.46.1.0037

Information

Published: 2021
First available in Project Euclid: 14 October 2021

Digital Object Identifier: 10.14321/realanalexch.46.1.0037

Subjects:
Primary: 26A15 , 46E30

Keywords: modulus of continuity , Riemann sums , symmetric spaces

Rights: Copyright © 2021 Michigan State University Press

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Vol.46 • No. 1 • 2021
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