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
Criterion for uniform distribution of sequences and a class of Riemann integrable functions
Tibor Šalát (1987)
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A note on Riemann integrability.
Beer, G.A. (1978)
International Journal of Mathematics and Mathematical Sciences
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Nonstandard analysis and generalized Riemann integrals
Jean Mawhin (1986)
Časopis pro pěstování matematiky
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Generalized multiple Perron integrals and the Green-Goursat theorem for differentiable vector fields
Jean Mawhin (1981)
Czechoslovak Mathematical Journal
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Weaker forms of continuity and vector-valued Riemann integration
M. A. Sofi (2012)
Colloquium Mathematicae
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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.