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

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

2012-03-26

arxiv.org/abs/1203.5625v3

Mathematics

Functional Analysis

4 pages

Scientific paper

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 follow as easy
consequences from our construction.

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