This article is cited in 2 papers

The integral analog of a series with a two-point sum range

O. S. Osipov

Tomsk State University, Tomsk

Abstract: We consider an improper integral corresponding to the series with a two-point sum range which was constructed by Kornilov in the space of integrable functions. We verify that the sum range of the integral is equal to the set of all constant functions.

Keywords: rearrangement of a series, rearrangement of an integral, Lebesgue–Bochner integral, sum range of a series, sum range of an improper integral.

UDC: 517.521

Received: 03.04.2008
Revised: 16.09.2009

 English version: Siberian Mathematical Journal, 2009, 50:6, 1062–1069

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