SUFFICIENT CONDITIONS FOR CONVERGENCE OF RIEMANN SUMS FOR FUNCTION SPACE DEFINED BY THE k-MODULUS OF CONTINUITY

Igor E. Preobrazhenskii

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SUFFICIENT CONDITIONS FOR CONVERGENCE OF RIEMANN SUMS FOR FUNCTION SPACE DEFINED BY THE k-MODULUS OF CONTINUITY

机译：通过k-模量连续性定义的函数空间的riemann和升温条件的充分条件

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摘要

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.

机译：对于由连续性的第k个模式定义的函数的类别，给出了对称空间x的规范，给出了在一组大量测量上的riemann和riemann和序列的两个成员的差异的估计。根据空间X的基本函数给出估计。使用该结果，对于来自给定对称空间的函数f，给出了足够的条件，即用于Lebesgue积分的riemann和riemann序列的序列的几乎无处不在的融合给定的函数。

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来源
《Real analysis exchange》 |2021年第1期|37-50|共14页
作者
Igor E. Preobrazhenskii;
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作者单位

Centre of Integrable Systems P.G. Demidov Yaroslavl State University Russia;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Riemann sums; symmetric spaces; modulus of continuity;

机译：riemann sums;对称空间;连续性模量;

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SUFFICIENT CONDITIONS FOR CONVERGENCE OF RIEMANN SUMS FOR FUNCTION SPACE DEFINED BY THE k-MODULUS OF CONTINUITY

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