[Probability Primer] {Measure theory}

(PP 1.1) Measure theory: Why measure theory - The Banach-Tarski Paradox

 

 

ball -> tear down to pieces -> rigid transformation (translation/rotation) -> two balls identical to the original one

 

 two ways to resolve the paradox

 

 

 

 

 

(PP 1.2) Measure theory: Sigma-algebras

 

 

 

proof of 3:

 

 

 

 

 

(PP 1.3) Measure theory: Measures

 

 

 

 

 

 

 

(PP 1.4) Measure theory: Examples of Measures

 

father of modern probability theory

 

 

 

three example of probability measure