Spatial-Temporal Differentiation Theorems
Idris Assani, Aidan Young

TL;DR
This paper investigates the conditions under which spatial-temporal averages of functions over shrinking sets in ergodic dynamical systems converge to the expected value, extending differentiation theorems in this context.
Contribution
It establishes new differentiation theorems for ergodic systems, linking the convergence of averages over shrinking sets to the measure-theoretic integral of functions.
Findings
Convergence of averages over shrinking sets under ergodicity.
Conditions for differentiation theorems in spatial-temporal settings.
Extension of classical differentiation results to dynamical systems.
Abstract
Let be a dynamical system where is a compact metric space with Borel -algebra , and is a probability measure that's ergodic with respect to the homeomorphism . We study the following differentiation problem: Given and , where and , when can we say that
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Topics in Algebra · Advanced Banach Space Theory
