Part II is devoted to a multidimensional quadrature formulas. Here are studied of a function of many variables. The presentation of a more concise and designed to a high mathematical level of the reader.
In spite of these differences, I am convinced that these parts should be presented together. On the one hand, it cannot be assumed that the specialist who is interested in multidimensional quadratures familiar with the functions of the Haar. On the other hand, it is hardly reasonable (but possible) to convince the reader that the functions of the Haar may be useful for applied mathematics, not indicating the most important (yet) application - the study of multidimensional quadrature.
In the book touches upon the issues which may be of interest to mathematicians very different specialties. With this in mind, I tried to reduce the dependence between some sections of the book (but not at the cost of repetition) , and even gave chapters 1, 2 and 3 separate pointers literature. The table on page 6 will help readers to highlight these issues.
Persons who are interested in only a "recipe" for the computation of multidimensional integrals, may apply directly to the section 4, ch. 6.
I first learned about the functions of the Haar from a course of lectures ETC. E. Menshov "Series of orthogonal functions",