nonameisfinetoo
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 May 11 awarded Supporter May 6 accepted Multiple ergodic averages with varying number of terms May 6 comment Multiple ergodic averages with varying number of terms Overcomplicating indeed. Thank you. May 5 comment Multiple ergodic averages with varying number of terms You're perfectly right, weak-mixing is the good working hypothesis. As for more expedient ways to prove that $f=0$ a.e.: For integers $n$ and $p$, $f_{n+p} \leq f_n S^n (f_p)$ so that when $p \rightarrow \infty$ and considering that $f_n \leq f_1$, the inequality $f \leq f_1 S^n (f)$ holds for all $n$. Taking averages and integrals, one finds that $\int f \leq 1/n \sum_{k=0}^n \int f_1 S^k (f) \rightarrow \int f_1 \int f$ so that $\int f \leq \int f_1 \int f$ which proves that $f=0$ almost everywhere. But this does not help for the convergence of $\sum f_n$ unless I am missing something? May 5 awarded Editor May 5 revised Multiple ergodic averages with varying number of terms added 18 characters in body; edited title May 5 asked Multiple ergodic averages with varying number of terms Apr 11 awarded Scholar Apr 11 accepted Uniqueness of analytic continuation on a domain of C^n. Apr 11 awarded Student Apr 11 asked Uniqueness of analytic continuation on a domain of C^n. Apr 6 comment Convexity of a cone in CxC Indeed. thank you. Apr 6 asked Convexity of a cone in CxC