Definition
Measure
Let
be a measurable space. A measure is a function assigning a non-negative, possibly infinite size
to each measurable set , subject to:
- Empty set:
. - Countable additivity: for every sequence
of pairwise disjoint sets in , Thus the size of a countable union of non-overlapping measurable sets is the sum of their sizes. The triple
is a measure space; if , then is a probability measure.