(1) Functions of a Complex Variable (2) Intégrales de Lebesgue Fonctions d'Ensemble Classes de Baire (3) Functions of a Complex Variable

Abstract

(1) THIS is a competent translation of the last, substantially revised, edition of the original. Prof. Goursat needs no introduction to the mathematical public, so we content ourselves with directing attention to some of the features of this admirable course. The definition of analytic function coincides with Cauchys definition of fonction monogene; the properties of such functions are developed with great lucidity, and the student is easily led on to such ideas as power series, circles of convergence, Weierstrasss theory of analytic continuation, conformal representation, and so on. Riemanns surfaces are alluded to, but not discussed; the main outline follows Cauchy, and in this we think the author is judicious, because, however useful Riemanns surfaces are by their appeal to intuition, they are not easily realised by a beginner, and they have to be constructed in every special case by analytical methods.

(1) Functions of a Complex Variable.

Being part i of vol. ii. By Prof. E. Goursat. Translated by Prof. E. R. Hedrick and O. Dunkel. Pp. x + 259. (chicago and London: Ginn and Co., 1916.) Price 11s. 6d.

(2) Intégrales de Lebesgue. Fonctions dEnsemble. Classes de Baire.

By C. de la Vallée Poussin. Pp. viii + 151. (Paris: Gauthier-Villars et Cie, 1916.) Price 7 fr.

(3) Functions of a Complex Variable.

By T. M. MacRobert. Pp. xiv + 298. (London: Macmillan and Co., Ltd., 1917.) Price 12s. net.