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On a characterization of Gaussian distributions on Abelian groups by constancy of regression

G. M. Feldman

B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine

Abstract: This note gives a complete description of locally compact Abelian groups $X$ which are appropriate for characterizing Gaussian distribution by constancy of regression.

Keywords: locally compact Abelian group, Gaussian distribution, regression.

Received: 29.09.1997

DOI: 10.4213/tvp1565

 English version: Theory of Probability and its Applications, 1999, 43:3, 477–480

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