Sufficient conditions for convergence of Riemann sums for function space defined by the \(k\)-modulus of continuity

DOI10.14321/REALANALEXCH.46.1.0037zbMath1483.26005OpenAlexW4293509647WikidataQ114054016 ScholiaQ114054016MaRDI QIDQ2054547

Igor E. Preobrazhenskii

Publication date: 3 December 2021

Published in: Real Analysis Exchange (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/real-analysis-exchange/volume-46/issue-1/Sufficient-conditions-for-convergence-of-riemann-sums-for-function-space/10.14321/realanalexch.46.1.0037.full

zbMATH Keywords

symmetric spacesmodulus of continuityRiemann sums

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Integrals of Riemann, Stieltjes and Lebesgue type (26A42)

Cites Work

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• On the approximation of Lebesgue integrals by Riemann sums
• Notes on Fourier analysis. XIX. A remark on Riemann sums
• On Density of Perfect Sets‡
• Survey on Riemann sums
• Estimates for a uniform modulus of continuity of functions from symmetric spaces
• On Riemann sums and maximal functions in $ \mathbb R^n$
• An Arithmetic Property of Riemann Sums
• A correction theorem for functions with integral smoothness

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