Real variable contributions of G. C. Young and W. H. Young
Originally this article should accompany a 4 volume edition of selected works of William Henry and Grace Chisholm Young which should appear in BI-Wissenschaftsverlag. Unfortunately for our project this publisher was sold to Spectrum Verlag who cancelled that edition. Nevertheless we have been able to publish a 1 volume edition at the Presses Polytechniques et Universitaires Romandes in Lausanne (2000), edited by S. D. Chatterji and the reviewer (see the review in Zbl 0947.01020). Bruckner and Thomson give a very well written overview about the main achievements and the influence of the Youngs on some aspects of real analysis and the development until now. The topics they discuss are the following: inner limiting sets, \(G_\delta\)-sets, characterisation of derivaties, products of derivatives, cluster sets, Denjoy-Young-Saks-theorem, extensions of the mean value theorem. The spirit of this article is best expressed in citing the authors: ``Our focus in review shall be to present those moments in their (i.e. Youngs) work, when a truly original conception has arisen which then led to deeper pursuit by later analysts. As far as possible we shall trace many of their ideas from their sources through to the large real analysis literature that the Youngs can be considered as having inspired or anticipated''.
scientific article; zbMATH DE number 1740121
scientific article