Metrics, Norms And Integrals: An Introduction To Contemporary Analysis
Metrics, Norms and Integrals is a textbook on contemporary analysis based on the author's lectures given at the University of Melbourne for over two decades. It covers three main topics: metric and topological spaces, functional analysis, and the theory of the Lebesgue integral on measure spaces. This self-contained text contains a number of original presentations, including an early introduction of pseudometric spaces to motivate general topologies, an innovative introduction to the Lebesgue integral, and a discussion on the use of the Newton integral. It is thus a valuable book to inform and stimulate both undergraduate and graduate students.
- Paperback | 428 pages
- 152 x 228 x 24mm | 621.42g
- 13 Nov 2008
- World Scientific Publishing Co Pte Ltd
- Singapore, Singapore
Table of contents
Metrics and Topologies: Metric Spaces; Convergence and Completeness; Continuity; Topological Spaces; Compactness; Connectedness; Linear Analysis: Normed Spaces; Inner Product Spaces; Linear Operators and Functionals; Self-Adjoint Compact Operators; Functional Analysis; Integration: Measure Spaces; Abstract Lebesgue Integral; Integral on the Real Line; Construction of Measures; Product Measures; Lebesgue Spaces.