On $L^p$-spaces of functions with values in locally convex spaces

Matthieu F. Pinaud; Humberto Prado

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arXiv · 2605.30191

On $L^p$-spaces of functions with values in locally convex spaces

Matthieu F. Pinaud·Humberto Prado

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Abstract

We study Lusin-measurable functions with values in locally convex spaces. In particular, the behavior of pointwise limits of sequences of Lusin-measurable functions and exhibit pathological phenomena arising in the nonmetrizable setting. Moreover, we establish approximation and density results for $L^p$-spaces constructed with this notion of measurability, including the density of simple functions in Hausdorff locally convex spaces and convergence results obtained through dyadic approximations.

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BibTeX RIS

Matthieu F. Pinaud, Humberto Prado. 2026-05-28. On $L^p$-spaces of functions with values in locally convex spaces. https://arxiv.org/abs/2605.30191

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