McShane equi-integrability and Vitali’s convergence theorem

Jaroslav Kurzweil; Štefan Schwabik

Displaying similar documents to “McShane equi-integrability and Vitali’s convergence theorem”

The Vitali convergence theorem for the vector-valued McShane integral

Richard Reynolds, Charles W. Swartz (2004)

Mathematica Bohemica

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The classical Vitali convergence theorem gives necessary and sufficient conditions for norm convergence in the space of Lebesgue integrable functions. Although there are versions of the Vitali convergence theorem for the vector valued McShane and Pettis integrals given by Fremlin and Mendoza, these results do not involve norm convergence in the respective spaces. There is a version of the Vitali convergence theorem for scalar valued functions defined on compact intervals in $ℝ^{n}$ given by...

Beppo Levi's theorem for the vector-valued McShane integral and applications.

Swartz, Charles (1997)

Bulletin of the Belgian Mathematical Society - Simon Stevin

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An elementary proof of the theorem that absolute gauge integrability implies Lebesgue integrability

Timothy Myers (2010)

Czechoslovak Mathematical Journal

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It is commonly known that absolute gauge integrability, or Henstock-Kurzweil (H-K) integrability implies Lebesgue integrability. In this article, we are going to present another proof of that fact which utilizes the basic definitions and properties of the Lebesgue and H-K integrals.

Another Perron type integration in $n$ dimensions as an extension of integration of stepfunctions

Jiří Jarník, Jaroslav Kurzweil (1997)

Czechoslovak Mathematical Journal

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For a new Perron-type integral a concept of convergence is introduced such that the limit $f$ of a sequence of integrable functions $f_{k}$ , $k \in ℕ$ is integrable and any integrable $f$ is the limit of a sequence of stepfunctions $g_{k}$ , $k \in ℕ$ .

Displaying similar documents to “McShane equi-integrability and Vitali’s convergence theorem”

The Vitali convergence theorem for the vector-valued McShane integral

Beppo Levi's theorem for the vector-valued McShane integral and applications.

An elementary proof of the theorem that absolute gauge integrability implies Lebesgue integrability

Another Perron type integration in n dimensions as an extension of integration of stepfunctions

Another Perron type integration in $n$ dimensions as an extension of integration of stepfunctions