We say that a function f from [0,1] to a Banach space X is increasing with respect to E ⊂ X* if x* ∘ f is increasing for every x* ∈ E. A function is separately increasing if it is increasing in each variable separately. We show that if X is a Banach space that does not contain any isomorphic copy of c₀ or such that X* is separable, then for every separately increasing function with respect to any norming subset there exists a separately increasing function such that the sets of points of discontinuity of f and g coincide.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba62-1-7,
author = {Artur Michalak},
title = {On Some Properties of Separately Increasing Functions from [0,1]n into a Banach Space},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {62},
year = {2014},
pages = {61-76},
zbl = {1312.46033},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba62-1-7}
}
Artur Michalak. On Some Properties of Separately Increasing Functions from [0,1]ⁿ into a Banach Space. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 62 (2014) pp. 61-76. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba62-1-7/