In which spaces is every curve Lebesgue-Pettis integrable?

2012/07/25 by Heinrich von Weizsäcker, von Weizsäcker, Heinrich · 1 citation
Mathematics · Physics and Astronomy · #Advanced Banach Space Theory #Advanced Differential Geometry Research #math.FA #msc:46G10

paper · pdf · doi:10.48550/arxiv.1207.6034

The new title sounds better

arxiv created 2013/01/11 · arxiv updated 2013/01/14

Abstract

In a real locally convex Hausdorff space the closed convex hull of every metrizable compact set is compact if (and only if) every continuous curve has a Pettis integral with respect to Lebesgue measure. For such spaces there is a natural concept of Bochner integrals.

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