Miklos Schweitzer 1981_10
Source:
January 31, 2009
probabilityreal analysisfunctionSupportintegrationcomplex numbersprobability and stats
Problem Statement
Let be a probability distribution defined on the Borel sets of the real line. Suppose that is symmetric with respect to the origin, absolutely continuous with respect to the Lebesgue measure, and its density function is zero outside the interval [\minus{}1,1] and inside this interval it is between the positive numbers and (). Prove that there is no distribution whose convolution square equals .
T. F. Mori, G. J. Szekely