3 problems

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Pinsker's product decomposition conjecture for ergodic transformations
Let $(X,\mu)$ be a standard probability space and let $T:X\to X$ be an ergodic measure-preserving transformation. A measure-preserving transformation is a $K$ -transformation when e…
Conjectureopenentropy-theory ergodic-theory measure-preserving-dynamicsarXiv posted 3 days ago
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Halmos–von Neumann conjecture on reversibility of measure-preserving transformations
A measure-preserving transformation is isomorphic to its inverse if it is measure-theoretically isomorphic to the transformation obtained by reversing time. Halmos–von Neumann conj…
Conjectureopenergodic-theory measure-preserving-dynamicsarXiv posted 3 days ago
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Finite-product independence conjecture for measure-preserving dynamical systems
Let $\mathcal{F}$ be a family of subsets of the positive integers, and let a measure-preserving dynamical system (m.d.s.) be called $\mathcal{F}$ -independent when it has the indepe…
Conjectureopenergodic-theory independence measure-preserving-dynamicsarXiv posted 3 days ago

Pinsker's product decomposition conjecture for ergodic transformations