The Haar measure of a profinite n-ary group

Abstract

We prove that every profinite n-ary group (G,f) = der,b(G,•) has a unique Haar measure mp and further for every measurable subset A ⊆ G, we have mp(A) = m(A) = (n - 1)m - (A), where m and m - are the normalized Haar measures of the profinite groups (G,•) and the Post cover G - , respectively.