Timeline for Conditional probabilities are measurable functions - when are they continuous?
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| Apr 8, 2010 at 21:20 | comment | added | John Jiang | @Yemon: for your first example of independent coordinate variables, wouldn't the function f be constant? If I understood correctly Tom's definition of $f$, it is defined as $f(x') = P(|y-y_0| < \eta | x = x')$, where $(x,y)$ is a vector valued random variable, as opposed to the notation $f(\vec{x})$. Then if $x$ is independent of $y$, then clearly there is a version of conditional probability such that $P(|y-y_0| < \eta | x= x') = P(|y-y_0| < \eta)$. Isn't this a constant function? | |
| Jan 29, 2010 at 3:03 | history | answered | Yemon Choi | CC BY-SA 2.5 |