Displaying similar documents to “Arzela - Ascoli's Theorem for Riemann - Integrable Functions on Compact Spaces.”

Gauge Integral

Roland Coghetto (2017)

Formalized Mathematics

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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,...

A simplified multidimensional integral

Ágnes M. Backhausz, Vilmos Komornik, Tivadar Szilágyi (2009)

Czechoslovak Mathematical Journal

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We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained more quickly. We also give a characterization of the integrable functions and their primitives.

The Denjoy extension of the Riemann and McShane integrals

Jae Myung Park (2000)

Czechoslovak Mathematical Journal

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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...

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.