of results, a considerable amount of which has been organized and presented in the
present volume in useful and no doubt fertile form. The notion of vector measures
can be made central to a study of Banach-space-valued functions (series, integrals,
differentiation, R-N theorems), to the representation and classification of linear
operations between certain kinds of spaces, and the classification of Banach spaces.
This is the view presented by the authors of this work, who display very effectively
the interplay between properties of B and properties of vector measures taking their
values in 2?, to the understanding of which they have themselves contributed sub-
stantially in recent years. Those who now or in the future work with Banach-space-
valued functions or in the classification of geometric properties of Banach spaces,
as well as those who have done so in the past, should be grateful to Professors
Diestel and Uhl for their substantial contribution.
B. J. PETTIS