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Estimates of capacity of self-similar measures

Jozef Myjak, Tomasz Szarek (2002)

Annales Polonici Mathematici

We give lower and upper estimates of the capacity of self-similar measures generated by iterated function systems ( S i , p i ) : i = 1 , . . . , N where S i are bi-lipschitzean transformations.

Extensions of probability-preserving systems by measurably-varying homogeneous spaces and applications

Tim Austin (2010)

Fundamenta Mathematicae

We study a generalized notion of a homogeneous skew-product extension of a probability-preserving system in which the homogeneous space fibres are allowed to vary over the ergodic decomposition of the base. The construction of such extensions rests on a simple notion of 'direct integral' for a 'measurable family' of homogeneous spaces, which has a number of precedents in older literature. The main contribution of the present paper is the systematic development of a formalism for handling such extensions,...

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