On Fri, 29 Apr 2005, Marc LeBrun wrote:
But what is the Official Definition of "mean" anyway? Looking at mathworld, it would seem that we must have
Kermit Sigmon wrote several papers on topological "means". According to him a mean is a commutative idempotent topological groupoid. Of course, no associativity is assumed. He also considered what he called n-means, which have n-ary operations, symmetric in all arguments and satisfying f(x,x,...x) = x for all x. Mostly his papers were concerned with topological matters. Here are some of the titles: Sigmon, Kermit Cancellative medial means are arithmetic. Duke Math. J. 37 1970 Sigmon, Kermit Acyclicity of compact means. Michigan Math. J. 16 1969 111--115. Sigmon, Kermit Medial topological groupoids. Aequationes Math. 1 1968 217--234. Sigmon, Kermit On the existence of a mean on certain continua. Fund. Math. 63 1968 311--319. Sigmon, Kermit A note on means in Peano continua. Aequationes Math. 1 1968 no. 1-2, 85--86.