Timeline for Is total variation continuous?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 23, 2011 at 7:04 | vote | accept | zzzhhh | ||
| Feb 22, 2011 at 18:22 | comment | added | Ori Gurel-Gurevich | I'm really nor very good with books recommendations, but any rigorous book on probability theory should be helpful. Perhaps the following reformulation will help: the space is just $I=[0,1]$. $\mu$ is the Lebesgue measure restricted to $I$. $I_n$ is the set of all reals in $I$ whose $n$-th binary digit is 0. $\mu_n$ is twice the Lebesgue restricted to $I_n$, i.e. $\mu_n(A)=2\mu(A \cap I_n)$. Then for every measurable $A$ we have $\mu_n(A) \to \mu(A)$, but the total variation distance between any $\mu_n$ and $\mu$ is 1. | |
| Feb 22, 2011 at 10:40 | comment | added | zzzhhh | I refrained from asking what is total measure. Could you please refer me to a textbook containing conceptions like uniform measure, total measure so that I can understand your reply after reading it? Thanks! | |
| Feb 21, 2011 at 18:57 | comment | added | Ori Gurel-Gurevich | The uniform measure is the probability measure of total measure 1, and for each $i$, $\mathbb{P}(x_i=0)=\frac12$ independently. | |
| Feb 21, 2011 at 11:00 | comment | added | zzzhhh | Sorry but what is the uniform measure? | |
| Feb 20, 2011 at 6:00 | history | answered | Ori Gurel-Gurevich | CC BY-SA 2.5 |