For every invertible mixing probability-preserving transformation and every fixed finite tuple of bounded measurable functions, consecutive multiple ergodic averages converge almost everywhere, along all positive averaging lengths, to the product of the functions’ integrals.
For every invertible mixing probability-preserving transformation and every fixed finite tuple of bounded measurable functions, consecutive multiple ergodic averages converge almost everywhere, along all positive averaging lengths, to the product of the functions’ integrals.
For every invertible mixing probability-preserving transformation and every fixed finite tuple of bounded measurable functions, consecutive multiple ergodic averages converge almost everywhere, along all positive averaging lengths, to the product of the functions’ integrals.
If correct, establishes almost-everywhere convergence for all finite lengths under ordinary mixing alone.
Do all consecutive multiple ergodic averages converge pointwise for mixing transformations?
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OpenAI reports pointwise multiple ergodic convergence for mixing transformations
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