ON THE MEASURE THEORETIC STRUCTURE OF COMPACT-GROUPS

If G is a compact group with w(G) = a greater than or equal to omega, we show the following results: (i) There exist direct products [GRAPHI CS] of compact metric groups and continuous open surjections [GRAPHICS ] with respect to Haar measure; and (ii) the Haar measure on G is Bair e and at the same time Jordan Isomorphic to the Haar measure on a dire ct product of compact Lie groups. Applications of the above results in measure theory are given.