Newbetuts

Prove that for any $\epsilon >0$ there exists a measurable set $E$ such that $m(E)<\infty$ and $\int_E f>(\int f)-\epsilon$.

If $X_t = Y_t$ in distribution, for any $t \in T$ (compact), is it true that $\mathbb E \sup_{t \in T} X_t = \mathbb E\sup_{t \in T} Y_t$?

Does this random variable have a density?

If a Radon measure is a tempered distribution, does it integrate all Schwartz functions?

Every open subset $O$ of $\Bbb R^d,d \geq 1$, can be written as a countable union of almost disjoint closed cubes.

Why is the Plancherel measure interesting?

Completeness of $\{ f_n : n \in \mathbb N \} \subset C[0,1]$ in $L^1[0,1]$

Azuma's inequality to McDiarmid's inequality?

proof that convergence in mean implies convergence in probability

An Application of Lebesgue Dominated Convergence Theorem

Showing that $\int_{X}\log(f)d\mu\le \mu(X)\log{1\over \mu (X)}$ without using Jensen's inequality

Sum of sets of measure zero

Fattened volume of a curve

If $f'(x)>0$ on $E$ , where $m(E)>0,$ then $m(f(E))>0$

The smallest $\sigma$-algebra in $X=\{1,2,3,4\}$ that contains a collection of subsets of $X$

Understanding proof that a integrable function on general measure space is finite almost everywhere

When is $L^1 = (L^\infty)^\ast$?

New posts in measure-theory

Generate the smallest $\sigma$-algebra containing a given family of sets

Composition of measurable & continuous functions, is it measurable?

Equivalent ideas of absolute continuity of measures

Prove that for any $\epsilon >0$ there exists a measurable set $E$ such that $m(E)<\infty$ and $\int_E f>(\int f)-\epsilon$.

If $X_t = Y_t$ in distribution, for any $t \in T$ (compact), is it true that $\mathbb E \sup_{t \in T} X_t = \mathbb E\sup_{t \in T} Y_t$?

Does this random variable have a density?

If a Radon measure is a tempered distribution, does it integrate all Schwartz functions?

Every open subset $O$ of $\Bbb R^d,d \geq 1$, can be written as a countable union of almost disjoint closed cubes.

Why is the Plancherel measure interesting?

Completeness of $\{ f_n : n \in \mathbb N \} \subset C[0,1]$ in $L^1[0,1]$

Azuma's inequality to McDiarmid's inequality?

proof that convergence in mean implies convergence in probability

An Application of Lebesgue Dominated Convergence Theorem

Showing that $\int_{X}\log(f)d\mu\le \mu(X)\log{1\over \mu (X)}$ without using Jensen's inequality

Sum of sets of measure zero

Fattened volume of a curve

If $f'(x)>0$ on $E$ , where $m(E)>0,$ then $m(f(E))>0$

The smallest $\sigma$-algebra in $X=\{1,2,3,4\}$ that contains a collection of subsets of $X$

Understanding proof that a integrable function on general measure space is finite almost everywhere

When is $L^1 = (L^\infty)^\ast$?