Abstract. We formalize and discuss a concept of mean value on a locally compact abelian group. We show that most of the classical notions of a mean value arising in mathematical analysis (e.g., integration on a compact group, the mean value for periodic functions, the mean value for almost periodic functions, etc.) are only various particular expressions of a great unity.

AMS Subject Classification (1991): 43A07; 28A25, 28C10

Keyword(s): Mean value, locally compact abelian groups

Received October 17, 2001, and in revised form October 7, 2002. (Registered under 2894/2009.)