Vol. 64, No. 2, 1976

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Averaging strongly subadditive set functions in unimodular amenable groups. II

William Richard Emerson

Vol. 64 (1976), No. 2, 353–368

This paper continues work initiated in Part I. The central question is one of characterizing a net {Aα} of Borel sets in the group G which averages a so-called regular set function S on G in the sense that λ(Aα)1S(Aα) has a limit (depending only on S), where λ is Haar measure. In Part I a sufficient condition for {Aα} to always average was derived; here we show that a “natural” relaxation of this condition is no longer sufficient for all regular S, at the same time essentially characterizing those S which may still be averaged. Moreover, the role of Følner summing sequences is considered in this context. Finally, properties of regular set functions are derived which may be of independent interest.

Mathematical Subject Classification 2000
Primary: 43A07
Received: 16 October 1975
Revised: 30 January 1976
Published: 1 June 1976
William Richard Emerson