Timeline for Zero correlation of all functions of random variables implying independence
Current License: CC BY-SA 4.0
4 events
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| Jan 11, 2021 at 14:59 | comment | added | jld | Is that second comment true? Since $Q := \{(-\infty, q] : q \in \mathbb Q\}$ is a $\pi$-system that generates the Borel $\sigma$-algebra, if $\mathbf 1_{A}(X)$ is uncorrelated with $\mathbf 1_B(Y)$ for every $A,B \in Q$ then $X \perp Y$, and that's a countable collection of indicators | |
| Jan 9, 2021 at 23:17 | comment | added | Richard Hardy | Thank you for the answer. Could you perhaps digest it to a more direct answer to my original question? | |
| Jan 9, 2021 at 18:03 | comment | added | whuber♦ | This characterization looks like a great way to prove two variables are not independent, though. | |
| Jan 9, 2021 at 17:59 | history | answered | Acccumulation | CC BY-SA 4.0 |