I am wondering if the Lebesgue measure of the union of a countable collection of disjoint measurable sets is equal to the sum of the measure of such sets. I feel that they may be equal. I know that for finite case they are equal. I know that for outer measure, the previous statement is wrong, e.g., (non measurable)Vitali set. How about collections of disjoint measurable set, are they always equal? What if I change the collection into an uncountable collection of Lebesgue measurable sets, are they equal?