Introductory Real Analysis
DSA ADS Course - 2021
Introductory Real Analysis - Kolmogorov and Fomin
Basic one-year course in real analysis.
The first four chapters present basic concepts and introductory principles in set theory, metric spaces, topological spaces, and linear spaces. The next two chapters consider linear functionals and linear operators, with detailed discussions of continuous linear functionals, the conjugate space, the weak topology and weak convergence, generalized functions, basic concepts of linear operators, inverse and adjoint operators, and completely continuous operators. The final four chapters cover measure, integration, differentiation, and more on integration. Special attention is here given to the Lebesque integral, Fubini's theorem, and the Stieltjes integral.
Each individual section — there are 37 in all — is equipped with a problem set, making a total of some 350 problems, all carefully selected and matched.