Exercises in Analysis Part 1 /

• Κύριοι συγγραφείς: Gasińksi, Leszek (Συγγραφέας), Papageorgiou, Nikolaos S. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Σειρά: Problem Books in Mathematics,
• Θέματα: Mathematics.; Functional analysis.; Measure theory.; Probabilities.; Topology.; Functional Analysis.; Measure and Integration.; Probability Theory and Stochastic Processes.

 Exercises in Analysis will be published in two volumes. This first volume covers problems in five core topics of mathematical analysis: metric spaces; topological spaces; measure, integration, and Martingales; measure and topology; and functional analysis. Each of five topics correspond to a different chapter with inclusion of the basic theory and accompanying main definitions and results, followed by suitable comments and remarks for better understanding of the material. At least 170 exercises/problems are presented for each topic, with solutions available at the end of each chapter. The entire collection of exercises offers a balanced and useful picture for the application surrounding each topic.   This nearly encyclopedic coverage of exercises in mathematical analysis is the first of its kind and is accessible to a wide readership. Graduate students will find the collection of problems valuable in preparation for their preliminary or qualifying exams as well as for testing their deeper understanding of the material. Exercises are denoted by degree of difficulty. Instructors teaching courses that include one or all of the above-mentioned topics will find the exercises of great help in course preparation. Researchers in analysis may find this Work useful as a summary of analytic theories published in one accessible volume. 

 1. Metric Spaces -- 2. Topological Spaces -- 3. Measure, Integral, and Martingales -- 4. Measures and Topology -- 5. Functional Analysis -- Other Problem Books -- List of Symbols -- Index.