Weaker forms of continuity and vector-valued Riemann integration
Volume 129 / 2012
Colloquium Mathematicum 129 (2012), 1-6
MSC: Primary 46G10; Secondary 46G12.
DOI: 10.4064/cm129-1-1
Abstract
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.
