@article{Hu2023, 
author = {Yiheng Hu and Gang Lyu and Yuanfeng Jin and Qi Liu},
title = {Exploration of indispensable Banach-space valued functions},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {11},
pages = {27670-27683},
keywords = {essential bounded Banach-valued function, sequential compactness, uniform convergence},
url = {https://www.sciopen.com/article/10.3934/math.20231416},
doi = {10.3934/math.20231416},
abstract = {In the paper, we present a necessary and sufficient condition for the existence of a sequence of measurable functions with finite values, which converge to any given essential bounded function in the topology of essential supremum in a Banach space. A new convergence method is proposed, which allows for the discovery of an essential bounded function    F that is valued in a Banach space. Generally speaking, there exists a Banach-valued essential bounded function    F which        F    n   can't converge to    F in the topology of essential supremum for any sequence of finite-valued measurable function.}
}