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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Displaying similar documents to “The Vitali convergence theorem for the vector-valued McShane integral”
Beppo Levi's theorem for the vector-valued McShane integral and applications.
McShane equi-integrability and Vitali’s convergence theorem
Jaroslav Kurzweil, Štefan Schwabik (2004)
Mathematica Bohemica
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The McShane integral of functions defined on an -dimensional interval is considered in the paper. This integral is known to be equivalent to the Lebesgue integral for which the Vitali convergence theorem holds. For McShane integrable sequences of functions a convergence theorem based on the concept of equi-integrability is proved and it is shown that this theorem is equivalent to the Vitali convergence theorem.
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.
A scalar Volterra derivative for the PoU-integral
V. Marraffa (2005)
Mathematica Bohemica
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A weak form of the Henstock Lemma for the -integrable functions is given. This allows to prove the existence of a scalar Volterra derivative for the -integral. Also the -integrable functions are characterized by means of Pettis integrability and a condition involving finite pseudopartitions.