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2021 ON THE SL-INTEGRAL OF LCTVS-VALUED FUNCTIONS
Rodolfo E. Maza, Sergio R. Canoy
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Real Anal. Exchange 46(2): 505-522 (2021). DOI: 10.14321/realanalexch.46.2.0505

Abstract

A function F:[a,b]X is said to be an SL function if it satisfies the Strong Lusin (SL) condition given as follows: for every θ-nbd U and a set E[a,b] of measure zero, there exists a gauge δ such that for every δ-fine partial partition D={([xi-1,xi],ti):1in} of [a,b] with tiE, there exist θ-nbds U1,U2,,Un such that i=1nUiV and F(xi)-F(xi-1)Ui for each i=1,2,,n. In this paper, we introduce the SL integral of a function taking values on a locally convex topological vector space (LCTVS). Further, we show that this integral is equivalent to a stronger version of the Henstock integral.

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Rodolfo E. Maza. Sergio R. Canoy. "ON THE SL-INTEGRAL OF LCTVS-VALUED FUNCTIONS." Real Anal. Exchange 46 (2) 505 - 522, 2021. https://doi.org/10.14321/realanalexch.46.2.0505

Information

Published: 2021
First available in Project Euclid: 8 November 2021

Digital Object Identifier: 10.14321/realanalexch.46.2.0505

Subjects:
Primary: ‎46G12
Secondary: 28B05 , 46A03

Keywords: locally convex topological vector spaces , SL-integral , Strong Luzin condition , Strongly Henstock Integral

Rights: Copyright © 2021 Michigan State University Press

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Vol.46 • No. 2 • 2021
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