New posts in lebesgue-measure

Let $f$ be a bounded measurable function on $E$. Show that there are sequences of simple functions converging uniformly on $E$.

real-analysis measure-theory lebesgue-measure

On the Lebesgue measure of a cartesian product

real-analysis measure-theory lebesgue-measure

Forming a subset of $\mathbb{R}$ by coin tossing

real-analysis probability-theory measure-theory lebesgue-measure

Lebesgue Integral Over Step Function

measure-theory lebesgue-measure riemann-integration measurable-functions

Difference of elements from measurable set contains open interval

real-analysis measure-theory lebesgue-measure

Prove the Countable additivity of Lebesgue Integral.

measure-theory lebesgue-integral lebesgue-measure

Characterization of a joining over a common subsystem.

functional-analysis measure-theory lebesgue-measure conditional-expectation ergodic-theory

Are dense subsets almost nothing or almost everything?

lebesgue-measure

A function that is Lebesgue integrable but not measurable (not absurd obviously)

lebesgue-integral lebesgue-measure

If $E$ has Lebesgue measure $0$, must there exist a translate such that $E\cap E+x=\varnothing$?

real-analysis measure-theory lebesgue-measure

Limit of lebesgue-integrable functions

measure-theory lebesgue-integral lebesgue-measure

Finding Lebesgue measure using Fubini's theorem

real-analysis lebesgue-measure

Show that there is an $F_\sigma$ set $F$ and $G_\delta$ set $G$ such that $F \subseteq E \subseteq G \text{ and } m^*(F)=m^*(E)=m^*(G).$ [duplicate]

real-analysis analysis measure-theory lebesgue-measure outer-measure

What examples are known of a dense and co-dense set of half measure?

real-analysis measure-theory lebesgue-measure

Proving this piecewise function is measurable.

measure-theory solution-verification lebesgue-measure

Show that there is a countable disjoint collection $\{ I_k \}_{k = 1}^{\infty}$ of intervals

measure-theory lebesgue-measure

Proving that $f$ is measurable with $f(x+y)= f(x)+f(y)$ then $f(x) =Ax$ for some $A\in\Bbb R$?

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

Applying Fubini's theorem for spherical coordinates

integration lebesgue-measure fubini-tonelli-theorems

If $f$ is Lebesgue integrable on $[0,2]$ and $\int_E fdx=0$ for all measurable set E such that $m(E)=\pi/2$. Prove or disprove that $f=0$ a.e.

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

A rigorous meaning of "induced measure"?

integration measure-theory lebesgue-integral lebesgue-measure