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Measure and integration. Part I. Measure theory. Vol. I, II. (Medida e integracion. Parte I. Teoria de la medida, Tomo I, II.) (Spanish) Zbl 0745.28001
Merida: Universidad de Los Andes, Facultad de Ciencias. xvii, 344 p./Tomo I; vii p., p. 345-708/Tomo II (1991).
This textbook (for a first course in measure theory) contains six chapters; in the first one the basic concepts about classes of sets and positive measures are presented, the second chapter is devoted to the outer measures and the metric outer measures. The complex measures on rings and \(\sigma\)-rings are studied in the third chapter where the extension of \(\sigma\)-finite measures and bounded complex measures, the Borel-Stieltjes and the Lebesgue-Stieltjes complex bounded measures on intervals are also considered. The chapter four deals with the Lebesgue measure on \(\mathbb{R}^ n\) while the fifth one studies the positive and complex Lebesgue-Stieltjes measures on \(\mathbb{R}^ n\), the treatment of the complex case (which can be adapted for the vector case) being quite original and new. The sixth chapter treats positive and complex Radon measures.
All the chapters include several solved problems and exercises. The proofs are developed in detail, in general the style is clear and didactic.

MSC:
28-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration
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