Remark

The calculation of the dual group of an infinite product of commutative compact groups is the object of Corollary 4 of II, p. 234 below. The case of a commutative locally compact group which is an arbitrary product of locally compact groups follows from these two statements, since in such a product, all the factors except a finite number are compact (TG, I, p. 66, prop. 14, b)).