Abstract
Abstract M. Das proved that the relative multifractal measures are mutually singular for the self-similar measures satisfying the significantly weaker open set condition. The aim of this paper is to show that these measures are mutually singular in a more general framework. As examples, we apply our main results to quasi-Bernoulli measures.
Highlights
Introduction and statements of resultsIn [4], Billingsley applies methods from ergodic theory to calculate the size of a level sets of the local dimension of μ with respect to another measure ν
Cole [6] has formalised these ideas by introducing a relative formalism for the multifractal analysis of one measure with respect to another
This formalism is based on the ideas of the "multifractal formalism" as clari ed by Olsen [15]
Summary
In [4], Billingsley applies methods from ergodic theory to calculate the size of a level sets of the local dimension of μ with respect to another measure ν. Cole [6] has formalised these ideas by introducing a relative formalism for the multifractal analysis of one measure with respect to another. This formalism is based on the ideas of the "multifractal formalism" as clari ed by Olsen [15]. The purpose of this paper is to show that the relative multifractal Hausdor and packing measures are mutually singular. The purpose of this paper is to study the multifractal structure of measures using the formalism introduced in [6]. The function q,t μ,ν is not necessarily countably subadditive, the set function monotone For these reasons, Cole introduced the packing and Hausdor measures denoted respectively by.
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