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arXiv · 1904.10928

Measurable regularity of infinite-dimensional Lie groups based on Lusin measurability

Natalie Nikitin
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Abstract

We discuss Lebesgue spaces $\mathcal{L}^p([a,b],E)$ of Lusin measurable vector-valued functions and the corresponding vector spaces $AC_{L^p}([a,b],E)$ of absolutely continuous functions. These can be used to construct Lie groups $AC_{L^p}([a,b],G)$ of absolutely continuous functions with values in an infinite-dimensional Lie group $G$. We extend the notion of $L^p$-regularity of infinite-dimensional Lie groups introduced by Gl\"ockner to this setting and adopt several results and tools.

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Natalie Nikitin. 2019-04-24. Measurable regularity of infinite-dimensional Lie groups based on Lusin measurability. https://arxiv.org/abs/1904.10928

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