Originally Posted by

**mgarson** Problems:

a. Let X be an in infinite set and let mu be a fnite outer measure on the

subsets of X such that every set {x}; x in X is mu-measurable and there

exists a countable subset A of X with mu(X\A) = 0. Show that mu is a

measure on the sigma-algebra of all subsets of X.

b) Let mu, vu be finite outer measures on X with the property in a), that is,

there exist countable sets A, B in X with mu(X\A) = vu(X\B) = 0.

Find the Lebesgue decomposition of vu with respect to mu.