Newbetuts

Are the measurable spaces $(\mathbb{R}^n, Bor(\mathbb{R}^n))$ and $(\mathbb{R}^m, Bor(\mathbb{R}^m))$ isomorphic for $n\neq m$

Example of application of Komlós theorem

$f(X)$ measurable, but $f$ not measurable

$\sigma$-finite measure and semi-finite measure

Exchangeability of inner product with the integral

Radon Nikodym Thm: extending to $\sigma$-finite case

Intersection of sets of positive measure

Measure - exercise 22 from Folland

Lebesgue Measurable Set which is not a union of a Borel set and a subset of a null $F_\sigma$ set?

Expected value of the size of set

A simpler proof of Jensen's inequality

For $f$ continuous and bounded find $\mathbb{E} \big [ \prod_{i=1}^n f \big (\ X_i \big ) \big ]$ for random variables $X_1, X_2, \ldots, X_n$

If $\tau$ is a stopping time with $\text P[\tau>s+t]=\text P[\tau>s]\text P[\tau>t]$, how do we determine the rate of the exponential distribution?

Question about an exercise in my Measure Theory book.

Convergence in $L_{\infty}$ norm implies uniform convergence

Mutually singular measures with the same support

New posts in measure-theory

What does it mean to sample, in measure theoretic terms?

Limit of the integral of a measurable function

How do I think of a measurable function?

What is "algebra" in $\sigma$-algebra (or "field" in $\sigma$-field)?

Are the measurable spaces $(\mathbb{R}^n, Bor(\mathbb{R}^n))$ and $(\mathbb{R}^m, Bor(\mathbb{R}^m))$ isomorphic for $n\neq m$

Example of application of Komlós theorem

$f(X)$ measurable, but $f$ not measurable

$\sigma$-finite measure and semi-finite measure

Exchangeability of inner product with the integral

Radon Nikodym Thm: extending to $\sigma$-finite case

Intersection of sets of positive measure

Measure - exercise 22 from Folland

Lebesgue Measurable Set which is not a union of a Borel set and a subset of a null $F_\sigma$ set?

Expected value of the size of set

A simpler proof of Jensen's inequality

For $f$ continuous and bounded find $\mathbb{E} \big [ \prod_{i=1}^n f \big (\ X_i \big ) \big ]$ for random variables $X_1, X_2, \ldots, X_n$

If $\tau$ is a stopping time with $\text P[\tau>s+t]=\text P[\tau>s]\text P[\tau>t]$, how do we determine the rate of the exponential distribution?

Question about an exercise in my Measure Theory book.

Convergence in $L_{\infty}$ norm implies uniform convergence

Mutually singular measures with the same support