MATHEMATICS

Integral analogs of series in Banach spaces

E. G. Lazareva^a, O. S. Osipov<sup>b

a</sup> Tomsk State University, Faculty of Mechanics and Mathematics
^b Solveig Multimedia Ltd.

Abstract: Integral analogs of conditionally convergent series in Banach spaces are investigated. The values range of an integral analog of a series is shown to be an affine subspace. It can be found by the way described in the Steinitz theorem about the sum range of series in finite-dimension spaces.

Keywords: integral analog of a series, rearrangement of a series, sum range of a series, values range of an integral.

UDC: 517.521


Accepted: May 22, 2010

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