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On Lp-spaces of functions with values in locally convex spaces
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 Lp-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
@misc{pinaud2026lpspaces,
title = {{On $L^p$-spaces of functions with values in locally convex spaces}},
author = {Matthieu F. Pinaud and Humberto Prado},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.30191},
eprint = {2605.30191},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.30191},
}
RIS
TY - UNPB
TI - On L^p-spaces of functions with values in locally convex spaces
AU - Matthieu F. Pinaud
AU - Humberto Prado
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2605.30191
UR - https://arxiv.org/abs/2605.30191
AB - 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.
ER -