INVARIANT MEASURE IN HOT GAUGE-THEORIES

We investigate the properties of the invariant measure for the A(0) ga uge field in finite temperature gauge theories both on the lattice and in the continuum theory. We find the cancellation of the measure cont ribution to the effective action by terms coming from the functional i ntegration over space-like fields. We present also arguments that the measure cancellation takes place in lattice theory. Arguments are base d on the very general form for the effective potential for the Polyako v loop. The spontaneous breakdown of Z(N) global symmetry is entirely due to the kinetic energy term of the gluonic interaction. We discuss the influence of the measure on the effective action, mechanism of-con finement and A(0) condensate.