A Mild Glimpse Into Measure Theory (2)
3. Measures and Outer measures
Let be a measurable space.
Definition: A measure on is a function such that:
(2) For all families of disjoint measurable sets,
- is allowed
- Property (2) is called -additivity
- We can also derive
Proposition 6 : Let , we have the following:
(1) If , then .
(2) If and , then
(4) If for all and for all , then .
(5) If for all and for all , then .
(6) If , then .
To be updated.