New posts in measure-theory

What is a Dynkin system? ($\lambda$-system)

real-analysis probability measure-theory descriptive-set-theory

Egorov's Theorem - Counterexample in Infinite Case

measure-theory examples-counterexamples

If $f$ is Lebesgue measurable on $[0,1]$ then there exists a Borel measurable function $g$ such that $f=g$ a.e.?

real-analysis analysis measure-theory examples-counterexamples

Almost Everywhere Convergence versus Convergence in Measure

real-analysis measure-theory convergence-divergence almost-everywhere

Does the set of differences of a Lebesgue measurable set contains elements of at most a certain length?

analysis measure-theory

Proof verification: To show that a function is not Lebesgue integrable.

real-analysis measure-theory continuity lebesgue-integral lp-spaces

Real analysis contradiction I cannot get rid of

real-analysis measure-theory cantor-set

Discontinuity points of a Distribution function [duplicate]

measure-theory probability-theory

Prove that Lebesgue measurable set is the union of a Borel measurable set and a set of Lebesgue measure zero

real-analysis measure-theory lebesgue-integral lebesgue-measure

Does the existence of the mean of a bounded, real-valued sequence imply it has a limiting distribution?

real-analysis sequences-and-series probability-theory measure-theory

Show that $g(x)=\int_{-\infty}^x f(t) \ dt$ is continuous.

real-analysis calculus measure-theory continuity

Is a measure for a sigma algebra determined by its values for a generator of the sigma algebra?

Let $A=\{(x,y) : x \in \mathbb{Q}, y \in \mathbb{R} \}$. Show that $m(A)=0$.

real-analysis measure-theory

For every $\epsilon>0$ there exists $\delta>0$ such that $\int_A|f(x)|\mu(dx) < \epsilon$ whenever $\mu(A) < \delta$

measure-theory lebesgue-integral

Prove that the sphere is the only closed surface in $\mathbb{R}^3$ that minimizes the surface area to volume ratio.

measure-theory differential-geometry

Intuition Wanted: Why Define Integrals Component-Wise

integration measure-theory intuition big-picture

A $\sigma$-algebra that is complete as a Boolean algebra?

measure-theory set-theory boolean-algebra

Convergence in measure and almost everywhere

real-analysis measure-theory convergence-divergence

Convergence in measure iff convergence in distance metric

real-analysis measure-theory convergence-divergence

Why $C_0^\infty$ is dense in $L^p$?

functional-analysis measure-theory