ON THE SL-INTEGRAL OF LCTVS-VALUED FUNCTIONS

IF 0.1 Q4 MATHEMATICS
Rodolfo Erodias Maza, Sergio Rosales Canoy
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引用次数: 1

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):1≤i≤n} of [a,b] with ti∈E, there exist θ-nbds U1,U2,…,Un such that ∑i=1nUi⊆V 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.
lctvs值函数的sl积分
如果函数F:[A,b]→X满足下述强Lusin (SL)条件,则称函数F:[A,b]→X是一个SL函数:对于测度为0的θ-nbd U和集合E∧[A,b],存在一个规范δ,使得对于[A,b]的每一个δ-细偏分区D={([xi-1,xi],ti):1≤i≤n},且ti∈E,存在θ-nbd U1,U2,…,Un使得∑i=1nUi≤≤V, F(xi)-F(xi-1)∈Ui,且对于每一个i=1,2,…,n。本文介绍了局部凸拓扑向量空间(LCTVS)上取值函数的SL积分。进一步,我们证明了这个积分等价于Henstock积分的一个更强的版本。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Real Analysis Exchange
Real Analysis Exchange MATHEMATICS-
CiteScore
0.40
自引率
50.00%
发文量
15
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