For X a subset of [0, 1], there is a family of properties which X might have, each of which is stronger than X having Lebesgue measure zero, and each of which is trivially satisfied if X is countable. The main properties in this family (apart from the Lusin-type conditions, which are really meant to be stated in conjunction with 2 s, =~r or with Martin's axiom--see section 1) are X has strong measure zero, i.e., if e0, el ..... en .... (n
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.