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

Abstract

We discuss Lebesgue spaces ${\mathcal{L}}^p([a,b],E)$ of Lusin measurable vector-valued functions and the corresponding vector spaces $A{C}_{L^p}([a,b],E)$ of absolutely continuous functions. These can be used to construct Lie groups $A{C}_{L^p}([a,b],G)$ 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 Glöckner to this setting and adopt several results and tools.

43 pages

Cited by in corpus (1)

• Lie groups of real analytic diffeomorphisms are $L^1$-regular