New posts in measure-theory

Is Dirichlet function Riemann integrable?

calculus real-analysis measure-theory lebesgue-integral riemann-integration

Vitali set proof: Why is $1 \leq \sum_{k \in \mathbb{N}}m(\mathcal{N}_k) \leq 3$ impossible?

measure-theory lebesgue-measure measurable-sets

What is the intuition behind Chebyshev's Inequality in Measure Theory

measure-theory inequality soft-question lebesgue-integral intuition

Integration with respect to counting measure.

weak convergence in $L^p$ plus convergence of norm implies strong convergence

analysis measure-theory

The construction of a Vitali set

Is there a change of variables formula for a measure theoretic integral that does not use the Lebesgue measure

measure-theory integration

Strictly increasing, absolutely continuous function with vanishing derivative

Çinlar's Probability and Stochastic, Examples 2.11 and 2.12

probability-theory measure-theory laplace-transform gamma-function

Does $f(x)$ is continuous and $f = 0$ a.e. imply $f=0$ everywhere?

real-analysis measure-theory

When does the integral vanish?

measure-theory lebesgue-integral

What is Haar Measure?

Lebesgue measurable but not Borel measurable

measure-theory lebesgue-measure examples-counterexamples

Is the image of a null set under a differentiable map always null?

For a set of positive measure there is an interval in which its density is high, $\mu(E\cap I)> \rho \mu(I)$

real-analysis measure-theory

Is composition of measurable functions measurable?

real-analysis measure-theory functions

Continuous functions are differentiable on a measurable set?

measure-theory descriptive-set-theory

Is Zorn's lemma applicable to this integration problem?

measure-theory lebesgue-integral ordinals

Continuity of $L^1$ functions with respect to translation

real-analysis measure-theory limits continuity lebesgue-integral

Can one construct a non-measurable set without Axiom of choice?

measure-theory set-theory axiom-of-choice