Abstract
for every continuous submultiplicative function b. This endowed with a natural topology is a complete locally convex space and it is a *-subalgebra of L1(G). One can prove that if G is first countable, then E(G) has a commutative approximate identity {ej}, n= 1, 2, . On the other hand every measure It on Xf(G) which defines an induced representation is a functional on E(G). It is a matter of simple computation to show that the vector
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