Displaying similar documents to “On variations of functions of one real variable”

On indefinite BV-integrals

Donatella Bongiorno, Udayan B. Darji, Washek Frank Pfeffer (2000)

Commentationes Mathematicae Universitatis Carolinae

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We present an example of a locally BV-integrable function in the real line whose indefinite integral is not the sum of a locally absolutely continuous function and a function that is Lipschitz at all but countably many points.

Riemann-type definition of the improper integrals

Donatella Bongiorno (2004)

Czechoslovak Mathematical Journal

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Riemann-type definitions of the Riemann improper integral and of the Lebesgue improper integral are obtained from McShane’s definition of the Lebesgue integral by imposing a Kurzweil-Henstock’s condition on McShane’s partitions.

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...