Analyse III. Calcul intégral. (Analysis III. Integral calculus). Nouvelle éd. corr. Nouvelle éd. corr. (Analyse III. Calcul intégral.) (French) Zbl 0920.00002

Schwartz, Laurent

Collection Enseignement des Sciences. 44. Paris: Hermann. 452 p. (1998).

This is the third volume of a completely revised edition of the author’s “Cours d’analyse” (see Zbl 0872.54001 and Zbl 0920.00001 for the first and second volumes). This volume includes Chapter V (Measure Theory).
Contents: Chapter V. Measure Theory: \(\S 1\) Riemann integral on the real axis; \(\S 2\) Measurable spaces and exterior measure; \(\S 3\) Upper integral associated to a positive measure; \(\S 4\) Radon measures on a locally compact space; \(\S 5\) Upper integral associated to a positive Radon measure; \(\S 6\) Measurable functions and convergence in measure; \(\S 7\) Vector-valued integrable functions; \(\S 8\) \(L^p\)-spaces; \(\S 9\) Vector measures; \(\S 10\) The Lebesgue-Radon-Nikodym theorems and duality; \(\S 11\) A measure associated to a map and a given measure; \(\S 12\) Fubini-type theorems; \(\S 13\) Weak convergence of measures.

Reviewer: C.Badea (Villeneuve d’Ascq)

MSC:

00A05	Mathematics in general
28-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration
26-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions
46-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis

Keywords:

textbook; measure theory; \(L^p\)-spaces

Citations:

Zbl 0920.00003; Zbl 0872.54001; Zbl 0920.00001