It was proved by Kadets that a weak*-continuous function on [0,1] taking values in the dual of a Banach space X is Riemann-integrable precisely when X is finite-dimensional. In this note, we prove a Fréchet-space analogue of this result by showing that the Riemann integrability holds exactly when the underlying Fréchet space is Montel.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm129-1-1,
author = {M. A. Sofi},
title = {Weaker forms of continuity and vector-valued Riemann integration},
journal = {Colloquium Mathematicae},
volume = {126},
year = {2012},
pages = {1-6},
zbl = {1267.46006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm129-1-1}
}
M. A. Sofi. Weaker forms of continuity and vector-valued Riemann integration. Colloquium Mathematicae, Tome 126 (2012) pp. 1-6. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm129-1-1/