Foundations of the theory of probability

viii Contents

V. ConditionalProbabilitiesandMathematical

Expectations

§

1. Conditionalprobabilities 47

§

2. ExplanationofaBorelparadox
   50

§3. Conditional

probabilities

withrespecttoarandomvari-

able 51

§

4. Conditional mathematicalexpectations 52

VI. Independence; TheLawofLargeNumbers

§

1. Independence
   57

§

2. Independentrandomvariables 58

§

3. TheLawofLargeNumbers 61

§

4. Notesontheconceptofmathematicalexpectation 64

§5.

The StrongLaw ofLarge Numbers

;

convergence

ofa

series 66

Appendix—Zero-or-onelawinthetheoryofprobability 69

Bibliography 71