Weaker forms of continuity and vector-valued Riemann integration

Tom 129 / 2012

M. A. Sofi Colloquium Mathematicum 129 (2012), 1-6 MSC: Primary 46G10; Secondary 46G12. DOI: 10.4064/cm129-1-1


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.


  • M. A. SofiDepartment of Mathematics
    Kashmir University, Hazratbal
    Srinagar - 190 006 J & K, India

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