Timeline for Prove that the finiteness of $E[X]$ is equivalent to the finiteness of $E[|X|]$
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 6 at 21:00 | comment | added | Sextus Empiricus | Ah, I can see how it follows from the definition, and it is more tautological than an inference. I was confused by the phrasing, "this shows", I thought I was missing something. | |
| Oct 6 at 20:46 | comment | added | User1865345 | What do you infer when $f$ is $\mu$-integrable? $f$ is $\mu$-integrable on $D$ if and only if both $\int_D f^+~\mathrm d\mu$ and $\int_D f^-~\mathrm d\mu$ are finite. This follows from the definition of integrability of $f.$ | |
| Oct 6 at 19:42 | comment | added | Sextus Empiricus | "which shows $|f|$ is $\mu$-integrable on $D.$" I don't see directly how it follows that '$|f|$ is integrable if $f$ is integrable' from the mere equation that splits up the integral into two integrals with unsigned functions. | |
| Oct 6 at 11:42 | comment | added | User1865345 | While these are universally used in the same sense throughout the literature and OP seems to be aware of that, for future readers, I have added their definition @SextusEmpiricus. | |
| Oct 6 at 11:39 | history | edited | User1865345 | CC BY-SA 4.0 |
added 40 characters in body
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| Oct 5 at 8:54 | history | answered | User1865345 | CC BY-SA 4.0 |