Descriptive characterizations of the integral by seminorms

2016/11/07 by Sokol Bush Kaliaj, Kaliaj, Sokol, Zenepe Shkoza +1
Computer Science · Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1611.02188

openalex publication_date 2016/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we first define the concept of the limit average range of a function defined on [0,1] and taking values in a Hausdorff locally convex topological vector space (locally convex space) X. Then, we present characterizations of the primitive F:[0,1] → X of an integrable by seminorms function f:[0,1] → X in terms of the limit average range of F. It is shown that the limit average range characterizes the integral by seminorms better then the usual differential.

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