Torbin G. Random variables of Jessen-Wintner's type andВtheir fractal properties

Thesis is devoted to investigation of random va-riables (r.v.) of Jessen-Wintner's type, that is to say.v., wish have pure distribution and being conver-ging serieses (with probability 1) of the discrete r.v. of the Jessen-One of the main problems of a thesis is the genera-lization and intensification of the Jessen-Wintner'stheorem. For achieve this aim the polybasic Q*-theorem. For achieve this aim the polybasic Q*-studied properties of this representation. It is shownthat with the help of Q*-representation it is easy todefine formally nowhere dense sets both zero and positivepositive measure of the Lebesgue, anomalouslyfractal and superfractal and internally fractal sets.