On functions whose improper Riemann integral is absolutely convergent
Christoph Klein (1987)
Studia Mathematica
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Displaying similar documents to “On Riemann integration of functions with values in topological linear spaces”
On functions whose improper Riemann integral is absolutely convergent
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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.