Hausdorff measures. With a foreword by K. Falconer. Paperback ed. (English) Zbl 0915.28002

Rogers, C. A.

Cambridge Mathematical Library. Cambridge: Cambridge University Press. xxvii, 195 p. (1998).

Hausdorff measures is a new edition, issued in the Cambridge Mathematical Library, of the remarkable book by C. A. Rogers, first published in 1970 (Zbl 0204.37601). This new edition contains an Appendix devoted to dimension print, a type of dimension introduced and studied by the author since 1988. Dimension prints provide a measure-theoretic way of distinguishing between different sets in Euclidean space having the same Hausdorff measure.
An excellent 20-pages foreword written by K. J. Falconer illuminates the historical and mathematical context of the development of the theory of Hausdorff measures. Especially is pointed out the impact of the Hausdorff measure on the development of the study of fractal sets, and it is suggested a comprehensive list of applications of Hausdorff measures. K. J. Falconer also includes a 5-pages list of references on Hausdorff measures and fractal geometry published since 1970, the year of the first publishing of Rogers’ book.
After 30 years, the book by Rogers is still a basic monograph on Hausdorff measures, written in an elegant and comprehensive way. It is indispensable for anyone whishing to introduce himself in the field of fractal geometry, and also to the researchers in this field.

Reviewer: E.Petrisor (Timişoara)

MSC:

28-02	Research exposition (monographs, survey articles) pertaining to measure and integration
28A78	Hausdorff and packing measures
01A75	Collected or selected works; reprintings or translations of classics
28A75	Length, area, volume, other geometric measure theory
28C15	Set functions and measures on topological spaces (regularity of measures, etc.)

Keywords:

metric measure; Hausdorff measure; Souslin sets; dimension prints

Citations:

Zbl 0204.37601