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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
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.

##### 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