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seen Aug 31 '11 at 15:40

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