Search records | 東京工業大学附属図書館蔵書検索

目次情報: 続きを見る

Preface

Notation and abbreviations

Finite trials / 1：

Probability spaces / 1.1：

Real random variables and random vectors / 1.2：

Mixing, direct composition, and tree composition / 1.3：

Conditional probabilities / 1.4：

Independence / 1.5：

Independent random variables / 1.6：

The law of large numbers / 1.7：

Probability measures / 2：

General trials and probability measures / 2.1：

The extension theorem of probability measures / 2.2：

Direct products of probability measures / 2.3：

Standard probability spaces / 2.4：

One-dimensional distributions / 2.5：

Characteristic functions / 2.6：

The weak topology in the distributions / 2.7：

D-Dimensional distributions / 2.8：

Infinite-dimensional distributions / 2.9：

Fundamental concepts in probability theory / 3：

Separable perfect probability measures / 3.1：

Events and random variables / 3.2：

Decompositions and o-algebras / 3.3：

Conditional probability measures / 3.4：

Properties of conditional probability measures / 3.6：

Real random variables / 3.7：

Conditional mean operators / 3.8：

Sums of independent random variables / 4：

General remarks / 4.1：

Convergent series of independent random variables / 4.2：

Central values and dispersions / 4.3：

Divergent series of independent random variables / 4.4：

Strong law of large numbers / 4.5：

Central limit theorems / 4.6：

The law of iterated logarithms / 4.7：

Gauss's theory of errors / 4.8：

Poisson's law of rare events / 4.9：

Index

Preface

Notation and abbreviations

Finite trials / 1：