It is self-contained, evenly paced, eminently readable, and readily accessible to those with adequate preparation in advanced calculus. 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. Each individual section -- there are 37 in all -- is equipped with a problem set, making a total of some problems, all carefully selected and matched. With these problems and the clear exposition, this book is useful for self-study or for the classroom -- it is basic one-year course in real analysis.
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Introductory Real Analysis