English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study natural measures on sets of beta-expansions and on slices throughself similar sets. In the setting of beta-expansions, these allow us to betterunderstand the measure of maximal entropy for the random beta-transformationand to reinterpret a result of Lindenstrauss, Peres and Schlag in terms ofequidistribution. Each of these applications is relevant to the study ofBernoulli convolutions. In the fractal setting this allows us to understand howto disintegrate Hausdorff measure by slicing, leading to conditions under whichalmost every slice through a self similar set has positive Hausdorff measure,generalising long known results about almost everywhere values of the Hausdorffdimension.

Sets of beta-expansions and the Hausdorff Measure of Slices through Fractals