The Equivalence of Some Bernoulli Convolutions to Lebesgue Measure
نویسنده
چکیده
Since the 1930’s many authors have studied the distribution νλ of the random series Yλ = ∑±λn where the signs are chosen independently with probability (1/2, 1/2) and 0 < λ < 1. Solomyak recently proved that for almost every λ ∈ [ 1 2 , 1], the distribution νλ is absolutely continuous with respect to Lebesgue measure. In this paper we prove that νλ is even equivalent to Lebesgue measure for almost all λ ∈ [ 1 2 , 1].
منابع مشابه
THE EQUIVALENCE OF SOME BERNOULLI CONVOLUTIONS TO LEBESGUE MEASURE by R
Since the s many authors have studied the dis tribution of the random series Y P n where the signs are are chosen independently with probability and Solomyak proved that for almost every the distribu tion is absolutely continuous with respect to Lebesgue measure In this paper we prove that is even equivalent to Lebesgue measure for almost all Mathematics Subject Classi cation Primary A A A Rese...
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