A probabilistic note on the Cauchy functional equation View Full Text


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Article Info

DATE

2019-04

AUTHORS

Sergey N. Smirnov

ABSTRACT

In this short note we show that a weak version of Bernstein’s characterization of the normal distribution implies the local integrability of a measurable solution of the Cauchy functional equation; the linearity of a solution of the Cauchy functional equation is an easy consequence of its local integrability. In its turn, this weak version of Bernstein’s theorem can be derived from Cauchy’s theorem. More... »

PAGES

445-449

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00010-018-0575-2

DOI

http://dx.doi.org/10.1007/s00010-018-0575-2

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1105252269


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