Kantorovich, the late Nobel Laureate, was a respected mathematical economist, and one of the founding fathers of linear programming. Part I begins with chapters on the theory of sets and real functions. Topics treated include universal functions, W.H. Young's classification, generalized derivatives of continuous functions and the H. Steinhaus problem. The book also includes papers on the theory of projective sets, general and particular methods of the extension of Hilbert space, and linear semi-ordered spaces. The author deals with a number of approximate calculations and solutions including a discussion of an approximate calculation of certain types of definite integrals, and also a method for the approximate solution of partial differential equations. In addition to this, the author looks at various other methods, including the Ritz method, the Galerkin method in relation to the reduction of differential equations and the Newton methods for functional equations. Towards the end of the book there are several chapters on computers.
On sequences of functions contained in W.H. Young's classification; on universal functions; on a problem of H. Steinhaus; on sequences of functions, continuous almost everywhere; on generalized derivatives of continuous functions; on two classes of operations on closed sets; on some theorems concerning the theory of projective sets; on certain general methods of the extension of Hilbert space; semi-ordered linear spaces and their application to the theory of linear operators; linear operators in semi-ordered spaces; the method of successive approximations for functional equations. (Part contents).