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

##### 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