G. Ye. Shilov 
Mathematical Analysis [PDF ebook] 
A Special Course

Mathematical Analysis: A Special Course focuses on the study of mathematical analysis. The book first discusses set theory, including operations on sets, countable sets, equivalence of sets, and sets of the power of the continuum. The text also discusses the elements of the theory of metric and normed linear spaces. Topics include convergent sequences and closed sets; theorem of the fixed point; normed linear spaces; and continuous functions and compact spaces. The selection also discusses the calculus of variations; the theory of the integral; and geometry of Hilbert space. The text also covers differentiation and integration, including functions of bounded variation, derivative of a non-decreasing function, differentiation of functions of sets, and the Stieltjes integral. The book also looks at the Fourier transform. Topics include convergence of Fourier series; Laplace transform; Fourier transform in the case of various independent variables; and quasi-analytic classes of functions. The text is a valuable source of data for readers interested in the study of mathematical analysis.