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We describe the limit measures for some class of deformations of the free convolution, introduced by A. D. Krystek and Ł. J. Wojakowski. In particular, we provide a counterexample to a conjecture from their paper.
Based on an analytical approach to the definition of multiplicative free convolution on probability measures on the nonnegative line ℝ+ and on the unit circle
we prove analogs of limit theorems for nonidentically distributed random variables in classical Probability Theory.
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