Real analysis / H.L. Royden, Stanford University, P.M. Fitzpatrick, University of Maryland, College Park.

Includes bibliographical references and index.

Chapter one The Real Numbers: Sets, Sequences, and Functions -- Chapter two Lebesgue Measure -- Chapter three Lebesgue Measureable Functions -- Chapter four Lebesgue Integration -- Chapter five Lebegue Integration: Further Topics -- Chapter six Differentiation and Integration -- Chapter seven The LP Spaces: Completeness and Approximation -- Chapter eight The LP Spaces: Duality and Weak Convergence -- Chapter nine Metric Spaces: General Properties -- Chapter ten Metric Spaces: Three Fundamental Theorems -- Chapter eleven Topological Spaces: General Properties -- Chapter twelve Topological Spaces: Three Fundamental Theorems -- Chapter thirteen Continuous Linear Operators Between Banach Spaces -- Chapter fourteen Duality for Normed Linear Spaces -- Chapter fifteen Compactness Regained: The Weak Topology -- Chapter sixteen Continuous Linear Operators on Hilbert Spaces -- Chapter seventeen General Measure Spaces: Their Properties and Construction -- Chapter eighteen Integration Over General Measure Spaces -- Chapter nineteen General LP Spaces: Completeness, Duality, and Weak Convergence -- Chapter twenty The Construction of Particular Measures -- Chapter twenty one Measure and Topology -- Chapter twenty two Invariant Measures

English