A uniformly continuous linear extension principle in topological vector spaces with an application to Lebesgue integration

2012/03/26 by Ben Berckmoes, Berckmoes, Ben
Computer Science · Mathematics · #28C05 #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Optimization and Variational Analysis #math.FA #msc:28C05

paper · pdf · doi:10.48550/arxiv.1203.5625

7 pages

openalex publication_date 2012/03/26 · arxiv created 2013/05/07 · arxiv updated 2013/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a uniformly continuous linear extension principle in topological vector spaces from which we derive a very short and canonical construction of the Lebesgue integral of Banach space valued maps on a finite measure space. The Vitali Convergence Theorem and the Riesz-Fischer Theorem are shown to follow as easy consequences from our construction.

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