Timeline for A term for sequences whose mean is defined?
Current License: CC BY-SA 3.0
11 events
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| Sep 25, 2015 at 1:48 | history | edited | Tony Huynh | CC BY-SA 3.0 |
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| Sep 25, 2015 at 1:22 | comment | added | Tony Huynh | I guess Cesàro summable is not a really good term when applied to a sequence. I think we used Cesàro convergent when I was an undergrad. Then again, a series is a sequence and vice versa. | |
| Sep 25, 2015 at 0:03 | comment | added | Tony Huynh | @jeq The sequence $1, 1, \dots, $ is Cesàro summable, with Cesàro limit $1$, but the series $\sum_i 1$ is not Cesàro summable. | |
| Sep 25, 2015 at 0:01 | comment | added | Tony Huynh | It is correct. The confusion is the distinction between a series and a sequence. In the wikipedia link provided by @jeq, Cesàro summability is defined as a property of sequences, while in my link above it is defined as a property of series. The property that the OP wants is that the sequence $a_i$ is Cesàro summable, not that the series $\sum a_i$ is Cesàro summable. | |
| Sep 25, 2015 at 0:00 | comment | added | jeq | The OP's question, I believe, was for a term for when the limit of a sequence of partial averages exists. The sequence $\lbrace 1,1,...\rbrace$ has a Cesàro mean, but is not Cesàro summable. | |
| Sep 24, 2015 at 23:47 | comment | added | user13113 | This answer is wrong, according to the wikipedia link. If $a_n$ was the sequence of partial sums of $\sum_k b_k$, then the limit the OP asks about is the Cesaro sum of $\sum_k b_k$. | |
| Sep 24, 2015 at 22:44 | history | edited | Tony Huynh | CC BY-SA 3.0 |
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| Sep 24, 2015 at 20:25 | comment | added | Tony Huynh | No, the Cesàro means are the sequence of partial averages. A sequence is Cesàro summable if the sequence of Cesàro means converges. | |
| Sep 24, 2015 at 20:24 | vote | accept | Tom Solberg | ||
| Sep 24, 2015 at 20:19 | comment | added | jeq | Perhaps Cesaro mean en.wikipedia.org/wiki/Ces%C3%A0ro_mean? | |
| Sep 24, 2015 at 20:07 | history | answered | Tony Huynh | CC BY-SA 3.0 |