Real analysis / H.L. Royden.
Material type:
TextLanguage: English Publication details: New York, London : Collier Macmillan ; 1968.Edition: 2nd edDescription: xvii, 444 p. : 25 cmISBN: - 0029794102 (pbk.)
- 515.8 ROY
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Gulbanoo Premji Library, Azim Premji University, Bengaluru | Martin Ravallion collection | 5th Floor | 515.8 ROY (Browse shelf(Opens below)) | Available | G53447 |
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| 515.352 KAR Advanced ordinary differential equations / | 515.62 ART Complementary variational principles / | 515.8 BAR The elements of real analysis / | 515.8 ROY Real analysis / | 516 ABB Teach yourself geometry / | 516 ABB Teach yourself geometry / | 516 ABB Teach yourself geometry / |
Includes bibliographical references (pages 435-436) and indexes.
I. Lebesgue integration for functions of a single real variable. Preliminaries on sets, mappings, and relations ; The real numbers: sets, sequences and functions ; Lebesgue measure; Lebesgue measurable functions ; Lebesgue integration ; Lebesgue integration : further topics ; Differentiation and integration ; The L[rho] spaces : completeness and approximation ; The L[rho] spaces : duality and weak convergence
II. Abstract spaces : metric, topological, Banach, and Hilbert spaces. Metric spaces : general properties ; Metric spaces : three fundamental theorems ; Topological spaces : general properties ; Topological spaces : three fundamental theorems ; Continuous linear operators between Banach spaces ; Duality for normed linear spaces ; Compactness regained : the weak topology ; Continuous linear operators on Hilbert spaces
III. Measure and integration : general theory. General measure spaces: their properties and construction ; Integration over general measure spaces ; General L[rho] spaces : completeness, duality and weak convergence ; The construction of particular measures ; Measure and topology ; Invariant measures
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