Measurable regularity of infinite-dimensional Lie groups based on Lusin measurability
read the original 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.
This paper has not been read by Pith yet.
Forward citations
Cited by 2 Pith papers
-
On $L^p$-spaces of functions with values in locally convex spaces
Defines L^p spaces via Lusin measurability for functions valued in locally convex spaces and establishes density of simple functions when the space is Hausdorff plus dyadic convergence results, while noting pathologie...
-
On $L^p$-spaces of functions with values in locally convex spaces
Defines L^p spaces via Lusin measurability for functions valued in locally convex spaces and proves density of simple functions plus dyadic approximation results in the Hausdorff case.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.