Year: 2026
Type: preprint
Abstract: Let $g$ be a nondecreasing left-continuous function and let $μ_g$ be its Lebesgue--Stieltjes measure. We establish a Banach-valued fundamental theorem of calculus and an Aubin--Lions compactness theorem for evolution measured by $μ_g$, allowing absolutely continuous, singular continuous and atomic components. If the range space has the Radon--Nikodým property, a curve is $g$-absolutely continuous if and only if it is an indefinite Bochner integral; its strong $g$-derivative is the Bochner density and the variation measure has density equal to its norm. A terminal atom may make the derivative invisible from the Bochner state class, so the natural evolution space is a graph of state--derivative pairs. For $B_0\Subset B\hookrightarrow B_1$, with $B_0$ and $B_1$ reflexive and $1
Source: arXiv (Cornell University)
Author: Fernández, Francisco J.
Institution: Universidade de Santiago de Compostela
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Xunta de Galicia
OpenAlex ID: W7212138755