Beschreibung:
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