Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 154-01. Pointwise Multiple Ergodic Averages for Mixing Transformations
Manuscript map · lines 5325–5334
OpenAI@2026-10-07#rem:oai-p-154-01
Authors: OpenAI. Family 154.
Title: Pointwise Multiple Ergodic Averages for Mixing Transformations.
Abstract: Let T be an invertible mixing probability-preserving transformation. For every integer n ≥ 2 and every fixed tuple of bounded measurable functions, we prove that the consecutive multiple ergodic averages of length n converge almost everywhere to the product of the integrals, as the averaging length tends to infinity through all positive integers. The probability space need not be standard, and no rate of mixing is required.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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