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A uniform boundedness principle of Pták

Charles W. Swartz — 1993

Commentationes Mathematicae Universitatis Carolinae

The Antosik-Mikusinski Matrix Theorem is used to give an extension of a uniform boundedness principle due to V. Pták to certain metric linear spaces. An application to bilinear operators is given.

Gauge integrals and series

Charles W. Swartz — 2004

Mathematica Bohemica

This note contains a simple example which does clearly indicate the differences in the Henstock-Kurzweil, McShane and strong McShane integrals for Banach space valued functions.

The Vitali convergence theorem for the vector-valued McShane integral

Richard ReynoldsCharles W. Swartz — 2004

Mathematica Bohemica

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 n given by Kurzweil and...

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