Precompactness in bivariate metric semigroup-valued bounded variation spaces
Functional Analysis
2025-01-07 v1
Abstract
In this paper, we show that if a set in bivariate metric semigroups-valued bounded variation spaces is pointwise totally bounded and joint equivariated then it is precompact. These spaces include bounded Jordan variation spaces, bounded Wiener variation spaces, bounded Waterman variation spaces, bounded Riesz variation spaces and bounded Korenblum variation spaces. To do so, we introduce the concept of equimetric set.
Cite
@article{arxiv.2501.02528,
title = {Precompactness in bivariate metric semigroup-valued bounded variation spaces},
author = {Jingshi Xu and Yinglian Niu},
journal= {arXiv preprint arXiv:2501.02528},
year = {2025}
}
Comments
bounded variation space; precompact set; metric semigroup; joint equivariated; bivariate; equimetric set