Abstract
Functions are investigated whose integrals over a given collection of sets are zero. Pompeiu sets are described in terms of the approximation of their indicators by linear combinations of the indicators of balls with special radii.
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References
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 10, pp. 1444–1448, October, 1993.
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Volchkov, V.V. On the Pompeiu problem and its generalizations. Ukr Math J 45, 1623–1628 (1993). https://doi.org/10.1007/BF01571095
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DOI: https://doi.org/10.1007/BF01571095