Measure

Let be a Measurable Space Let be a Countably Additive Set Function i.e.

• for any sequence of disjoint elements of :

Then is called a measure. The triple is called a Measure Space

Finite Measure sigma-finite Measure Probability Measure

Set Function Algebra Ring Carathéodory’s Extension Theorem Uniqueness of Measures Borel Sigma Algebra Lebesgue Measure