TITLE: What does it mean for a set to have Lebesgue measure zero?
QUESTION [40 upvotes]: I am studying examples of sets with Lebesgue measure zero (e.g. the Cantor Set) but wanted an intuitive description of what this means rather than a formal definition. Thank you.

REPLY [27 votes]: Practically speaking this means that when you integrate functions such sets don't matter, in the sense that if you modify the domain of integration by a set of measure zero, the integral is unchanged.