Boole inequality, proof of

Let {B1,B2,} be a sequence defined by:


Clearly Bi,i, since is σ-algebra, they are a disjoint family and :


and since P is a measure over it follows that :


Clearly BiAi , then P(Bi)P(Ai) because measures are, then it follows that :


finally taking n :


the latter is valid because the measure continuity , and is the proof of the theorem

Title Boole inequalityMathworldPlanetmath, proof of
Canonical name BooleInequalityProofOf
Date of creation 2013-03-22 15:47:18
Last modified on 2013-03-22 15:47:18
Owner Bunder (13010)
Last modified by Bunder (13010)
Numerical id 6
Author Bunder (13010)
Entry type Proof
Classification msc 60A99