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Non-existence of measurable solutions of certain functional equations via probabilistic approaches.
- Source :
- Aequationes Mathematicae; Aug2021, Vol. 95 Issue 4, p629-637, 9p
- Publication Year :
- 2021
-
Abstract
- This paper deals with functional equations in the form of f (x) + g (y) = h (x , y) where h is given and f and g are unknown. We will show that if h is a Borel measurable function associated with characterizations of the uniform or Cauchy distributions, then there is no measurable solutions of the equation. Our proof uses a characterization of the Dirac measure and it is also applicable to the arctan equation. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00019054
- Volume :
- 95
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Aequationes Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 151387252
- Full Text :
- https://doi.org/10.1007/s00010-021-00811-z