An Illustrative Introduction to Modern Analysis

ISBN-13: 9781138718272 / Angielski / Twarda / 2017 / 558 str.

Nikolaos Katzourakis; Eugen Varvaruca

Opis

Aimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis.

Spis treści

Sets, mappings, countability and choice. Metric spaces and normed spaces. Completeness and applications. Topological spaces and continuity. Compactness and sequential compactness. The Lebesgue measure on the Euclidean space. Measure theory on general spaces. The Lebesgue integration theory. The class of Lebesgue functional spaces. Inner product spaces and Hilbert spaces. Linear operators on normed spaces. Weak topologies on Banach spaces. Weak* topologies and compactness. Functional properties of the Lebesgue spaces. Solutions to the exercises.