Abstract Bayes' Formula and Conditional Expectation

Table of contents:

08:28 - A gentle introduction of Bayes’ formula
10:17 - Interpreting the Abstract Bayes’ in terms of Conditioning on Events
13:45 - An intuitive introduction of Abstract conditional expectation
16:56 - Interpreting the Conditional Expectation in terms of Conditioning on Events
20:48 - Interpreting the Cond Expectation in terms of Conditioning on Random Variable
24:14 - Formal definition of Conditional Expectation
28:23 - Definition of abstract Conditional Probability
30:50 - Formal proof of Bayes’ Formula

A correction: At 27:43 when it says \mu is absolutely continuous with respect to P, the reason should be: P[G]=0 means \mu[0]=0, and also at 26:11 please ignore the statement saying weaker/stronger!