Joys of Haar Measure

Joe Diestel, Kent State University, Kent, OH, USAAngela Spalsbury, Youngstown State University, Youngstown, OH, USA

• PrefaceLebesgue measure in Euclidean spaceMeasures on metric spacesIntroduction to topological groupsBanach and measureCompact groups have a Haar measureApplicationsHaar measure on locally compact groupsMetric invariance and Haar measureSteinlage on Haar measureOxtoby's view of Haar measureAppendix AAppendix BBibliographyAuthor indexSubject index

The book under review is a serious adventure in Measure Theory and not for the faint of heart. It is a wonderfully structured guide to some deep exploration of continuous quantity. At the heart of its exposition is the question of what it means to assign lengths, areas, volumes and hyper-volumes to abstract sets sitting somewhere in n-dimensional space." - MAA Online"The text under review, as the title suggests, is a somewhat unorthodoxly written exposition of the theory of Haar measure. The joyous manner in which the authors present the material is unique and original, and quite catchy. Under the skillful hands of the authors, the subject, which is already inherently beautiful and elegant, comes to life in a very entertaining fashion. The book is well aimed at the graduate level, both with respect to the level of detail given and with respect to the expected mathematical maturity at that stage... The exposition is filled with historical detail and, at times, different mathematical points-of-view, leading to a pleasantly well-rounded understanding of the material and an appreciation of certain aspects of its development. I find the book to be particularly well suited as a self-study book for the motivated student, as well as a supplementary book for any course on the topic." - Zentralblatt Math