New posts in lebesgue-measure

Lebesgue Measurable Set which is not a union of a Borel set and a subset of a null $F_\sigma$ set?

measure-theory lebesgue-measure examples-counterexamples descriptive-set-theory borel-sets

An outer measure is countable-additive on the measurable sets

real-analysis measure-theory lebesgue-measure

Prove that $m^*(A\cup B)=m^*(A)+m^*(B)$ whenever $\exists \alpha>0$ such that $|a-b|>\alpha$ for any $a\in A,b\in B$

analysis measure-theory lebesgue-measure outer-measure

$f_n^\alpha(x) = n^\alpha x^n$ converges almost everywhere

measure-theory lebesgue-measure pointwise-convergence

A function that is bounded and measurable but not Lebesgue integrable

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

If $\ \sum_{k=1}^n m(E_n) > n-1,$ then prove that $\bigcap_{k=1}^n E_k$ has positive measure.

real-analysis measure-theory lebesgue-measure

The subset that $m(E \cap I) \geq \alpha m(I)$ has measure 1.

measure-theory lebesgue-measure

If $ \int fg = 0 $ for all compactly supported continuous g, then f = 0 a.e.?

real-analysis functional-analysis lebesgue-integral lebesgue-measure almost-everywhere

Can we find uncountably many disjoint dense measurable uncountable subsets of $[0,1]$?

real-analysis lebesgue-measure

Why is the outer measure of the set of irrational numbers in the interval [0,1] equal to 1?

real-analysis analysis measure-theory proof-verification lebesgue-measure

Dirac delta distribution & integration against locally integrable function

functional-analysis measure-theory distribution-theory lebesgue-measure

Show that $\int|f(x)|dx=\int_0^\infty m(E_\alpha)d\alpha$

lebesgue-integral lebesgue-measure

Why "countability" in definition of Lebesgue measures?

measure-theory lebesgue-measure

Find $n$-dimensional measure of set $A$

measure-theory lebesgue-integral lebesgue-measure

Does a set with strictly positive Lebesgue measure contain an interval?

measure-theory lebesgue-measure

Is there a Lebesgue measurable subset $A \subset R$ such that for every interval $(a,b)$ we have $0 < \lambda(A\cap(a,b))< (b-a)$ [duplicate]

real-analysis measure-theory lebesgue-measure

Lebesgue space and weak Lebesgue space

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

Analytic sets are Lebesgue measurable

lebesgue-measure descriptive-set-theory

Converse for Fubini-Tonelli's theorem

measure-theory lebesgue-integral lebesgue-measure

"Lebesgue" measurabillity on Riemannian manifolds

real-analysis measure-theory lebesgue-measure smooth-manifolds