MathDB
Miklos Schweitzer 1981_10

Source:

January 31, 2009
probabilityreal analysisfunctionSupportintegrationcomplex numbersprobability and stats

Problem Statement

Let P P be a probability distribution defined on the Borel sets of the real line. Suppose that P P is symmetric with respect to the origin, absolutely continuous with respect to the Lebesgue measure, and its density function p p is zero outside the interval [\minus{}1,1] and inside this interval it is between the positive numbers c c and d d (c<d c < d). Prove that there is no distribution whose convolution square equals P P. T. F. Mori, G. J. Szekely