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.
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References
Kornilov P. A., “On the set of sums of a conditionally convergent series of functions,” Math. USSR-Sb., 65, No. 1, 119–131 (1990).
Kadets M. I. and Kadets V. M., Series in Banach Spaces: Conditional and Unconditional Convergence, Birkhäuser, Basel, Boston, and Berlin (1997).
Kashin B. S. and Saakyan A. A., Orthogonal Series [in Russian], Nauka, Moscow (1984).
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Original Russian Text Copyright © 2009 Osipov O. S.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 6, pp. 1348–1355, November–December, 2009.
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Osipov, O.S. The integral analog of a series with a two-point sum range. Sib Math J 50, 1062–1069 (2009). https://doi.org/10.1007/s11202-009-0117-1
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DOI: https://doi.org/10.1007/s11202-009-0117-1