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 adapt techniques of Hochman to prove a non-singular ergodic theorem for$\mathbb{Z}^d$-actions where the sums are over rectangles with side lengthsincreasing at arbitrary rates, and in particular are not necessarily balls of anorm. This result is applied to show that the critical dimensions with respectto sequences of such rectangles are invariants of metric isomorphism. Theseinvariants are calculated for a class of product actions.

Non-singular $\mathbb{Z}^d$-actions: an ergodic theorem over rectangles with application to the critical dimensions