On functions whose improper Riemann integral is absolutely convergent

Christoph Klein

Displaying similar documents to “On functions whose improper Riemann integral is absolutely convergent”

On Riemann integration of functions with values in topological linear spaces

Ch. Klein, S. Rolewicz (1984)

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Roland Coghetto (2017)

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Some authors have formalized the integral in the Mizar Mathematical Library (MML). The first article in a series on the Darboux/Riemann integral was written by Noboru Endou and Artur Korniłowicz: [6]. The Lebesgue integral was formalized a little later [13] and recently the integral of Riemann-Stieltjes was introduced in the MML by Keiko Narita, Kazuhisa Nakasho and Yasunari Shidama [12]. A presentation of definitions of integrals in other proof assistants or proof checkers (ACL2, COQ,...

On Riemann-type definition for the wide Denjoy integral

Piotr Sworowski (2011)

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The Denjoy extension of the Riemann and McShane integrals

Jae Myung Park (2000)

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In this paper we study the Denjoy-Riemann and Denjoy-McShane integrals of functions mapping an interval $[a, b]$ into a Banach space $X .$ It is shown that a Denjoy-Bochner integrable function on $[a, b]$ is Denjoy-Riemann integrable on $[a, b]$ , that a Denjoy-Riemann integrable function on $[a, b]$ is Denjoy-McShane integrable on $[a, b]$ and that a Denjoy-McShane integrable function on $[a, b]$ is Denjoy-Pettis integrable on $[a, b] .$ In addition, it is shown that for spaces that do not contain a copy of $c_{0}$ , a measurable Denjoy-McShane...

Criterion for uniform distribution of sequences and a class of Riemann integrable functions

Tibor Šalát (1987)

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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.