On the uniqueness of the branching parameter for a random cascade measure
G. Molchan
Abstract
An independent random cascade measure is specified by a random generator, a vector of dimension c with non-negative components. The dimension c is called the branching cascade parameter. It is shown under certain restrictions that, if this measure has two generators with a.s. positive components, and the ratio ln c1/ln c2 for their branching parameters is an irrational number, then this measure is a Lebesgue measure. In other words, when c is a power of an integer number p and the p is minimal for c, then a cascade measure that has the property of intermittency specifies p uniquely.
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