Analysis IV: Applications of measure theory. (Analyse IV: Applications à la théorie de la mesure. Avec la collab. de K. Zizi.) (French) Zbl 0920.00003

Schwartz, Laurent

Collection Enseignement des Sciences. 45. Paris: Hermann. 444 p. (1993).

This is the fourth and last volume of a completely revised edition of the author’s “Cours d’analyse” (see Zbl 0872.54001, Zbl 0920.00001 and Zbl 0920.00002 for the other volumes). This volume includes Chapter VI (Applications of Measure Theory).
Contents: Chapter VI. Applications of Measure Theory: \(\S 1\) Specific properties of Radon measures on the real axis; \(\S 2\) Multiple integrals on \(\mathbb{R}^n\); \(\S 3\) Functions represented by series or integrals; \(\S 4\) The convolution product on \(\mathbb{R}^n\); \(\S 5\) The Fourier transform; \(\S 6\) The exterior algebra of a vector space; \(\S 7\) Differential forms; \(\S 8\) Orientation of real manifolds; \(\S 9\) Integrating a differential form; \(\S 10\) Stokes’ formula; \(\S 11\) Computing integrals using residues; \(\S 12\) Eulerian functions and the Euler-McLaurin formula.

Reviewer: C.Badea (Villeneuve d’Ascq)

MSC:

00A05	Mathematics in general
28-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration
43-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to abstract harmonic analysis
44-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to integral transforms
46-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis

Keywords:

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

Citations:

Zbl 0920.00001; Zbl 0872.54001; Zbl 0920.00002