Tag Archives: Entropy

Tao’s Proof of (logarithmically averaged) Chowla’s conjecture for two point correlations

The Liouville function is the completely multiplicative function with for every prime . The Chowla conjecture predicts that this function behaves randomly. Here is a version of this conjecture. Conjecture 1 (Chowla) For every finite set , This conjecture received … Continue reading

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Entropy of measure preserving systems

A measure preserving system is a quadruple where is a set, is a -algebra, is a probability measure and is a measurable map satisfying for every . The notion of isomorphism in the category of measure preserving systems (defined, for … Continue reading

Posted in Classic results, Ergodic Theory, Tool | Tagged | 1 Comment