# Questions tagged [cesaro-summable]

For questions about Cesàro summation and Cesàro summable sequences.

22 questions
1answer
275 views

### What useful properties does usual summation have, but alternatives do not? (Cesaro, etc)

Before I really ask my question, I want to give my train of reasoning. Suppose we have some method of summation (as I understand, assigning a number to a series) that satisfies some or all of ...
1answer
242 views

0answers
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### Infinite/Recursive Cesàro Summation of $\zeta(1)$

Is anything known about this kind of `infinite' Cesàro summation (or any related types of summation)? If we have a function we wish to sum $f(n)$, but $$S^0[f] = \sum_{n=1}^\infty f(n)$$ diverges, ...
0answers
67 views

### Dominated convergence theorem for vairance and cesaro mean of random variables

I was wondering the following problem: If $X_n$ is a sequence of independent random variables, $|X_n|\leq b, (b>0)$ and $X_n$ converges to $X$ almost surely. Using dominated convergence theorem, ...
0answers
415 views