# Tagged Questions

Questions related to measures, sigma-algebras, measure spaces, Lebesgue integration and the like.

24 views

### measure of a set which is a subset of infinitely many subsets of probability measure space

Let $B,A_1,A_2,....$ be the subsets of a probability measure space. If $B \subset \bigcup A_j$, show that $m(B) \le \sum_{j=0}^\infty m(A_j)$. I have no idea as how to approach it. I do have the ...
69 views

19 views

52 views

### information measure for matrix that is analogous to rank

Is there a measure for matrix that is analogous to rank of the matrix, but it is continuous on matrix elements? Say, we could say the information in identity matrix $I_n$ is $n$, and when the off-...
28 views

### Show that if $E$ is Jordan measurable then $m(A-B) \leq \epsilon$ [on hold]

I want to show that if $E$ is Jordan measurable then $m(A-B) \leq \epsilon$ where $A \subset E \subset B$. I think I have the right ideas but feel I am missing some details. I'd like some feedback ...
47 views

13 views

24 views

### Hausdorff measure vs Lebesgue measure for a hypersurface in $\mathbb{R}^n$

Let $H$ be a compact smooth hypersurface with boundary in $\mathbb{R}^n$. We can compute the Lebesgue measure $\mathcal{L}(H)$ with respect to the induced Lebesgue measure coming from $\mathbb{R}^n$, ...
56 views

### another version of criterion for measurable set

Let $\mu^{\ast}$ be the outer measure on $R$.A collection $\left\{A_i\right\}$ is a partition of $R$ if $A_i \cap A_j=\phi$ if $i\neq j$ and $\bigcup^\infty_{i=1} A_i=R$. Prove that all sets on the ...
Let $X,Y$ be some nice measurable spaces (I'm interested in $[0,1]$ so we can assume compact, etc.). Let $\mu$ be a measure on $X\times Y$ (again, assume it's a nice probability measure, or even ...