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On $L^p$-spaces of functions with values in locally conve...
[Submitted on 28 May 2026 (v1), last revised 4 Sep 2026 (this ve · 2026-05-29 · via math updates on arXiv.org

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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.

Submission history

From: Matthieu Pinaud [view email]
[v1] Thu, 28 May 2026 16:33:20 UTC (11 KB)
[v2] Sun, 28 Jun 2026 23:34:11 UTC (12 KB)
[v3] Fri, 4 Sep 2026 16:33:23 UTC (14 KB)