ABSTRACT
Let (7 • x ' = - l < f < l , j c / = j£pbe the hyperplane cutting the sphere Sn
at height t from its centre along the (n — 2)-dimensional sphere orthogonal to the
vector x'. We introduce the mean of a function CJ(CT), defined on 5 n _ 1 , over the above
section. In the case n = 2 this is just the arithmetic mean over two points:
M u ( x ' , t ) = U ^ + 2
U l X - \ (4.1)
where
it) are given by
wil l be called the equatorial x'-mean of uj(a).
