@article{Wei2025, 
author = {Leilei Wei and Xia Zhang and Ming Liu},
title = {Bi-continuous semigroups on sequentially complete random Saks spaces},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {9},
pages = {5616-5637},
keywords = {random Saks spaces, bi-continuous semigroups, Hille-Yosida generation theorem, (ε, λ)-topology},
url = {https://www.sciopen.com/article/10.3934/era.2025250},
doi = {10.3934/era.2025250},
abstract = {In this paper, we first introduced the Riemann integral for an abstract-valued function from a finite closed real interval to a sequentially complete random Saks space and gave the fundamental theorem of calculus for an        L          0      -Lipschitz function. Then we investigated some important properties peculiar to bi-continuous semigroups on a sequentially complete random Saks space. Finally, based on the above work, we established the Hille-Yosida generation theorem for such bi-continuous semigroups, which extends and improves several known results.}
}