Displaying similar documents to “On Riemann-type definition for the wide Denjoy integral”

The McShane, PU and Henstock integrals of Banach valued functions

Luisa Di Piazza, Valeria Marraffa (2002)

Czechoslovak Mathematical Journal

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Some relationships between the vector valued Henstock and McShane integrals are investigated. An integral for vector valued functions, defined by means of partitions of the unity (the PU-integral) is studied. In particular it is shown that a vector valued function is McShane integrable if and only if it is both Pettis and PU-integrable. Convergence theorems for the Henstock variational and the PU integrals are stated. The families of multipliers for the Henstock and the Henstock variational...

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,...

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...

Adjoint classes of functions in the H 1 sense

Piotr Sworowski (2007)

Czechoslovak Mathematical Journal

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Using the concept of the H 1 -integral, we consider a similarly defined Stieltjes integral. We prove a Riemann-Lebesgue type theorem for this integral and give examples of adjoint classes of functions.