added to *ergodic theory* *this reference* which discusses applications of cohomology theory to the subject. This reminded me of David Corfield’s search for cohomological notions in “random” contexts, though maybe it’s not relevant, I am not sure.

I think that there is an encyclopaedia of mathematics and applications: dynamical systems (red cover, edit: or this was about operator algebras and dynamical systems? edit: no, it is very abstract one, I just peeked into it) which has large part dedicated to the shift-type dynamical systems. I had it in hands years ago, so I can not say about the particular result, but I would not be surprised to find it there.

Edit: I added a link to ergodic theory to one course page having some canonical references in ergodic theory.

]]>Speaking of this, I had wanted to get my hands on a proof that the shift transformation on the space of irrationals between 0 and 1, which sends a continued fraction $[a_1, a_2, a_3, \ldots]$ to $[a_2, a_3, \ldots]$, is ergodic with respect to the measure $\frac1{\log 2}\frac{d x}{1 + x}$. Any ideas where to find such a proof? (Might be nice for an article ergodic theory as well, since this measure space provides archetypal examples of chaotic phenomena, or so I sense.)

]]>New stub ergodic theory wanted at measure theory.

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