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

Authors: Matthieu F. Pinaud, Humberto Prado

math.FA2026-05v1license

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.

Cite

@article{arxiv.2605.30191,
  title  = {On $L^p$-spaces of functions with values in locally convex spaces},
  author = {Matthieu F. Pinaud and Humberto Prado},
  journal= {arXiv preprint arXiv:2605.30191},
  year   = {2026}
}

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