Countable Subadditivity
If is a collection in , then .
Proposition 2.1 (Countable Subaddivity)
If is a collection in , i.e. , then
Proof
Define and for . Then is a disjoint collection in with , and for every . Countable additivity therefore gives
Related
Stated in
- Proposition 2.1 (Countable Subaddivity)§2.1 Probability Measure