TITLE: What is the difference between outer measure and Lebesgue measure?
QUESTION [46 upvotes]: What is the difference between outer measure and Lebesgue measure?
We know that there are sets which are not Lebesgue measurable, whereas we know that outer measure is defined for any subset of $\mathbb{R}$.

REPLY [2 votes]: Lebesgue  outer measure (m*) is for  all set E of real numbers where as Lebesgue measure (m) is only for the set the set of measurable set of real numbers  even if both of them are set fuctions.
by Geleta Tadele Mohammed