Answer to Question #262925 in Real Analysis for kavya

Question

prove that A set of measure zero need not be null set.

Answer 1

In measure theory, a null set refers to a set of measure zero. For example, in the reals, R with its standard measure (Lebesgue measure), the set of rationals Q has measure 0, so Q is a null set in R. Actually, all finite and countably infinite subsets of R have measure 0. In contrast, the empty set always refers to the unique set with no elements.