Definition
Whole-space Axiom
Let
. The whole-space axiom requires Thus the family contains the entire underlying space. It is one of the defining axioms of a sigma algebra.
Contrast
Membership of the whole space is the boundary
Let
. Compare
- Holds:
contains . - Fails:
does not contain . Although the members of
collectively cover , their union is not itself a member. The whole-space axiom requires explicitly.