New posts in measure-theory

Let $A\subset\mathbb{R}$ a measurable and bounded set. Show that exists for each $0<\alpha<1$ an interval $I$ such that $m(A\cap I)/m(I)>\alpha$.

real-analysis analysis measure-theory lebesgue-measure

Show that the Cantor set is nowhere dense

real-analysis measure-theory lebesgue-measure cantor-set

Proof of $E[Y]=\int_0^x nX^{n-1}(1-F_X(x))dx$ for $Y=X^n$ [duplicate]

probability-theory measure-theory

Do integrable functions vanish at infinity? [duplicate]

Must the (continuous) image of a null set be null?

real-analysis analysis measure-theory

Measurable subset of Vitaly set has measure zero. Proof.

measure-theory lebesgue-measure

Is $Y$, obtained from a random uniform unitary, uniformly distributed?

measure-theory transformation unitary-matrices haar-measure

Prove that $X,Y$ are independent iff the characteristic function of $(X,Y)$ equals the product of the characteristic functions of $X$ and $Y$

probability-theory measure-theory characteristic-functions

Do the subsets of $\mathbb N$ that have asymptotic density form an algebra?

measure-theory lebesgue-measure

Radon-Nikodym derivative as a measurable function in a product space

Total Variation and indefinite integrals

real-analysis measure-theory lebesgue-integral bounded-variation

Two notions of total variation norms

analysis measure-theory probability-theory

Uniform estimate for the boundary area of the union of closed unit balls

geometry measure-theory geometric-measure-theory

Lebesgue measurable subset of $\mathbb{R}$ with given metric density at zero

Proof that the Cardinality of Borel Sets on $\mathbb R$ is $c$ without using the ordinals .

real-analysis measure-theory descriptive-set-theory borel-sets

“Most intuitive” average of $P$ for all $x\in A \cap [a,b]$, where $A\subseteq\mathbb{R}$?

integration measure-theory lebesgue-measure intuition average

Important examples of measures which are not $\sigma$-finite

measure-theory soft-question big-list

Convergence in norm but not almost everywhere of $f_{t_n}=f(\cdot-t_n)$ to $f$

real-analysis measure-theory lp-spaces

Can locally "a.e. constant" function on a connected subset $U$ of $\mathbb{R}^n$ be constant a.e. in $U$?

real-analysis general-topology measure-theory

How to show product of two nonmeasurable sets is nonmeasurable?

real-analysis measure-theory