Royden H., Fitzpatrick P. Real Analysis 5ed 2023

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Royden H., Fitzpatrick P. Real Analysis 5ed 2023

Textbook in PDF format Halsey L. Royden's Real Analysis has contributed to educating generations of mathematical analysis students. The 5th. Edition of this classic text presents some important updates while presenting the measure theory, integration theory and elements of metric, topological, Hilbert and Banach spaces that a modern analyst should know. Part I continues to consider Lebesgue measure and integration for functions of a real variable. In this revision, the treatment of general measure and integration is moved to Part II rather than Part III; material formerly in Part II is placed in Part III and a brief Part IV. This brings measure and integration on Euclidean space closer to their origin, the case of real variables; it also presents the opportunity to foreshadow more strongly, in the context of general measure and integration, concepts which later appear in general spaces. The text assumes an undergraduate course on the fundamental concepts of analysis. Preface (Patrick M. Fitzpatrick). 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 Lp Spaces: Completeness and Approximation. The Lp Spaces: Duality, Weak Convergence, and Minimization. Measure and Integration: General Theory General Measure Spaces: Their Properties and Construction. Particular Measures. Integration over General Measure Spaces. General Lp Spaces: Completeness, Convolution, and Duality. Abstract Spaces: Metric, Topological, Banach, and Hilbert Spaces Metric Spaces: General Properties. Metric Spaces: Three Fundamental Theorems and Applications. 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. Measure and Topology: Invariant Measures Measure and Topology. Bibliography Index