-1
$\begingroup$

Which set I say that it's measurable set, and which one is a Lebesgue measurable set !!! I read that the Set which is applied on Lebesgue measure is a sequence of small intervals. so what about the general measure. To be clear, what's the diff between the outer measure and Lebesgue outer measure?

$\endgroup$
2
$\begingroup$

Given a $\sigma$-algebra $\mathcal{F}$ on a set $\Omega,$ we say that the sets $A\in\mathcal{F}$ are $\mathcal{F}$-measurable.

In this Wikipedia entry, you can see how an outer measure is defined, and how an outer measure gives rise to a $\sigma$-algebra of measurable sets, for which the measure equals the outer measure (by definition).

Both concepts can then be specialized to the case of Lebesgue outer measure/ Lebesgue measurable sets by taking the appropriate notion of outer measure.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.