Functional Analysis: A First Course Pdf

Integration theory and general topology form the core of this textbook for a first-year graduate course in real analysis. After the foundational material in the first chapter (construction of the reals, cardinal and ordinal numbers, Zorn's lemma and transfinite induction), measure, integral and topology are introduced and developed as recurrent themes of increasing depth. The treatment of integration theory is quite complete (including the convergence theorems, product measure,

by Alexander A Balinsky (Author), W Desmond Evans (Author), Roger T. Lewis (Author)
Focuses throughout on versions of the inequalities in Lp spaces
Shows how Hardy, Sobolev and Cwikel-Lieb-Rosenbljum inequalities are intimately related
Is the first textbook to systematically cover multidimensional Hardy-type inequalities

Authors: Gasiński, Leszek, Papageorgiou, Nikolaos S.
​Contains exercises ranging from easy to difficult, with level of difficulty designated
Features an encyclopedic volume of exercises in five core topics of mathematical analysis
Prepares students well for qualifying exams and tests their depth of understanding of the material