Weil-Nachbin Theory for Locally Compact Groups

Abstract

Assume H is a normal subgroup of the locally compact group G with measures  and  the on G and H , respectively, and assume : m G R   is a continuous homomorphism from G to a group R  of positive real numbers with the operation of multiplication, then we establish that for the existence of a measure  on the quotient group / GH , it is necessary and sufficient that       rr HG h m h h    holds for all hH  so that each m -relatively invariant measure on / GH is a quotient measure /      ; also, we show that the m -relatively invariant measure  on /