I have two Skellam-distributed random variables, $X_1$ and $X_2$, with rate parameters $\mu_{1,+}, \mu_{1,-}$ and $\mu_{2,+}, \mu_{2,-}$ respectively. (For my case, it just so happens that their distributions are symmetric, i.e. $\mu_{1,+} = \mu_{1,-}$ and $\mu_{2,+} = \mu_{2,-}$.) Now I want t...

Ex 1.1.9 in Tao's An introduction to measure theory asks us to show that any compact convex polytope in $\mathbb{R}^d$ is Jordan measurable. Is the following an efficient (or even valid) approach to the problem? Show that every $d$-dimensional solid simplex is Jordan measurable; and Show that a...

This is for homework: if $A,A'$ are two elementary sets containing $E$, bounded set in $\mathbf{R}^d$, then $m(A)-m^*(A \backslash E)$ is equal to $m(A')-m^*(A \backslash E)$ So far my goal has been to show that they're both equal to the expression for $A \cap A'$ which is another elementary set...