New posts in outer-measure

Constructing an outer measure on a set whose measurable sets are exactly a given sigma algebra on the set.

measure-theory outer-measure

Problems with Set Function

measure-theory average means outer-measure amenability

$G$ be a non-measurable subgroup of $(\mathbb R,+)$ ; $I$ be a bounded interval , then $m^*(G \cap I)=m^*(I)$?

real-analysis group-theory measure-theory outer-measure

If the measure of union = sum of outer measures, then the sets are measurable

measure-theory outer-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

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

Extension of measure is less or equal to outer measure when restricted to semiring [closed]

measure-theory outer-measure

Prove $\mu^*(A)=\nu(A)$ if there exists a cover $A\subset \cup_{n\geq1} B_n$ and $\mu^*(B_n)<\infty \;\forall n\geq 1$

measure-theory outer-measure

Why is the inner measure problematic?

measure-theory definition lebesgue-measure motivation outer-measure

If $E\in \mathscr{M}_{\mu^*}$ , then for each $\varepsilon$ exists $A\in \mathscr{A}$ such that $\mu^*(A\triangle E)< \varepsilon$

measure-theory outer-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

Does Sigma Algebra Necessarily Induce a Measure?

real-analysis measure-theory outer-measure

The Motivation of Pre-measure for Construction of Measures

real-analysis measure-theory outer-measure