Generalization and New Proof for Almost Everywhere Convergence to Imply Local Convergence in Measure

Yu-Lin Chou

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arXiv · 2005.06988

Generalization and New Proof for Almost Everywhere Convergence to Imply Local Convergence in Measure

Yu-Lin Chou

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Abstract

With a new proof approach we prove in a more general setting the classical convergence theorem that almost everywhere convergence of measurable functions on a finite measure space implies convergence in measure. Specifically, we generalize the theorem for the case where the codomain is a separable metric space and for the case where the limiting map is constant and the codomain is an arbitrary topological space.

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BibTeX RIS

Yu-Lin Chou. 2020-04-27. Generalization and New Proof for Almost Everywhere Convergence to Imply Local Convergence in Measure. https://arxiv.org/abs/2005.06988

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