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arXiv · 1203.5625

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

Ben Berckmoes
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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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Ben Berckmoes. 2013-05-07. A uniformly continuous linear extension principle in topological vector spaces with an application to Lebesgue integration. https://arxiv.org/abs/1203.5625

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