New posts in lebesgue-measure

Convergence of a series of translations of a Lebesgue integrable function

real-analysis measure-theory convergence-divergence lebesgue-integral lebesgue-measure

Why do we work on the Borel sigma algebra and not on the Lebesgue sigma algebra?

measure-theory lebesgue-measure borel-sets

for each $\epsilon >0$ there is a $\delta >0$ such that whenever $m(A)<\delta$, $\int_A f(x)dx <\epsilon$

integration measure-theory lebesgue-integral lebesgue-measure

Minkowski Content

measure-theory intuition geometric-measure-theory lebesgue-measure

Non-measurable sets and sigma-algebra definition

measure-theory soft-question terminology lebesgue-measure

Why this definition for Lebesgue measurable functions?

lebesgue-measure

(Integral) Operator Norm: Find $||\phi||$ where $\phi : \mathcal{L^1(m)} \to \mathbb{R}$ is defined by $\phi(f) = \int (x - \frac{1}{2}) f(x) dm(x)$

measure-theory operator-theory lebesgue-integral lebesgue-measure

convolution of characteristic functions

measure-theory lebesgue-measure convolution

Is there a decreasing sequence of sets in $\mathbb{R}^{n}$ with these outer-measure properties?

real-analysis measure-theory lebesgue-measure examples-counterexamples outer-measure

Proof that the Lebesgue measure is complete

measure-theory lebesgue-measure

If a set $E\subset [a,b]$ has possitive measure, then $x-y\in \mathbb{R\setminus Q}$

measure-theory solution-verification lebesgue-measure

Sufficiency of Lebesgue's Criterion for Riemann Integrability

real-analysis proof-explanation lebesgue-measure riemann-integration

Is the set $\{ \int_0^x f\,\mathrm d\lambda\mid f(x)=0\}$ a Lebesgue-null set for $f\geq0$?

lebesgue-integral lebesgue-measure absolute-continuity

Measure of image of critical points set is equal 0

real-analysis measure-theory lebesgue-measure

Topology of convergence in measure

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

Measure of set where holomorphic function is large

complex-analysis analysis lebesgue-measure entire-functions

Vestrup Measure and Integration Exercise 5.1.6

real-analysis measure-theory lebesgue-measure measurable-functions

Convergence in measure implies pointwise convergence?

measure-theory convergence-divergence lebesgue-measure

Non-invertible measure preserving transformations of $\mathbb{R}^n$

measure-theory lebesgue-measure

Let $\lambda(A)$ be the Lebesgue measure of $A$. There exists an interval $I$ such that $\lambda(E \cap I) / \lambda(I) < 1-\epsilon$

measure-theory lebesgue-measure