- set of interest for measure theory (we may refer to it as the sample space) - subsets of the sample space. - families of subsets. - infimum of sequence of sets. - supremum of sequence of sets - is the limit of the sequence of sets . - is the limit of the sequence of sets . - infinitely often
- monotonically non-decreasing - strictly non-decreasing - monotonically non-increasing - strictly non-increasing
- a -algebra - a -algebra generated by - the Borel algebra on . - where and this denotes