Real analysis /
Royden, H. L.,
Real analysis / H.L. Royden. - 2nd ed. - New York, London : Collier Macmillan ; 1968. - xvii, 444 p. : 25 cm.
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
0029794102 (pbk.)
Functions of real variables.
Functional analysis.
Measure theory.
515.8 / ROY
Real analysis / H.L. Royden. - 2nd ed. - New York, London : Collier Macmillan ; 1968. - xvii, 444 p. : 25 cm.
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
0029794102 (pbk.)
Functions of real variables.
Functional analysis.
Measure theory.
515.8 / ROY