This article, with the second part to issue in the same review, forms an introductory part of a forthcoming paper concerning the analysis of structure of statistical inference. The fundamental concepts of measure-theoretical probability theory such as measure on σ-field of sets, extension theorems on measure and Lebesgue-Stieltjes integral are discussed in the parts I and II. The final object of the author in this series of papers is to make the fact clear that probability space is a mathematical model to be tested both from various points of view and by various procedures of test, and to point out the deductive character of statistical inference which is sometimes misconceived as if it were inductive.

名誉教授宮崎友愛先生記念論文集