a branch of mathematics that studies generalized notions of volumes
Terminology
measure - a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size. In this sense, a measure is a generalization of the concepts of length, area, and volume
measure zero - a set of measure zero occupies no volume in the space we are measuring
almost everywhere - a property that holds almost everywhere holds throughout all of the space except for on a set of measure zero