Pt. 1 Mathematical Introduction
Sets of Points 3
Theory of Measure and Integration in R[subscript 1] 19
Theory of Measure and Integration in R[subscript n] 76
Various Questions 89
Pt. 2 Random Variables and Probability Distributions
Foundations 137
Variables and Distributions in R[subscript 1] 166
Variables and Distributions in R[subscript n] 260
Pt. 3 Statistical Inference
Generalities 323
Sampling Distributions 341
Tests of Significance, I 416
Theory of Estimation 473
Tests of Significance, II 525
Table 1 The Normal Distribution 557
Table 2 The Normal Distribution 557
Table 3 The x[superscript 2]-Distribution 559
Table 4 The t-Distribution 560
List of References 561
Index 571

In this classic of statistical mathematical theory, Harald Cramér joins the two major lines of development in the field: while British and American statisticians were developing the science of statistical inference, French and Russian probabilitists transformed the classical calculus of probability into a rigorous and pure mathematical theory. The result of Cramér's work is a masterly exposition of the mathematical methods of modern statistics that set the standard that others have since sought to follow.
For anyone with a working knowledge of undergraduate mathematics the book is self contained. The first part is an introduction to the fundamental concept of a distribution and of integration with respect to a distribution. The second part contains the general theory of random variables and probability distributions while the third is devoted to the theory of sampling, statistical estimation, and tests of significance.

Harald Cramér (1893-1985) was professor of actuarial mathematics and mathematical statistics and director of the Institute of Mathematical Statistics at the University of Stockholm.