Riemann sums and modular functions on locally compact groups

作     者：Ross, KA Willis, G 

作者机构：Univ Oregon Eugene OR 97403 USA Univ Newcastle Callaghan NSW 2308 Australia 

出 版 物：《PACIFIC JOURNAL OF MATHEMATICS》 (Pac. J. Math.)

年 卷 期：1997年第180卷第2期

页      面：325-331页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：.Haar measure fails Riemann sums modular functions locally compact group Jessen theorem 

摘      要：In 1967 the first author and Karl Stromberg published a theorem concerning generalized limits of Riemann sums on locally compact groups. The setting is a locally compact group G and an increasing sequence H-n of closed subgroups whose union is dense in G. The theorem was shown to hold provided that the restriction of the modular function on G to H-n agrees with the modular function of H-n for all large n. This hypothesis holds in many cases and, in fact, Ross and Stromberg were unable to determine whether the hypothesis was really needed for the theorem or even whether this hypothesis always holds. An example is provided which shows that this hypothesis does not always hold. It is then shown that the theorem fails without the hypothesis.