  The familiar generating functionals in QFT fail to be true measures since the
Lebesgue measure in infinite-dimensional spaces is not defined in general. The
problem lies in constructing representations of topological $^*$-algebras of
quantum fields which are not normed. We restrict our consideration only to
chronological forms on quantum field algebras. In this case, since
chronological forms of boson fields are symmetric, the algebra of quantum
fields can be replaced with the commutative tenzor algebra of the corresponding
infinite-dimensional nuclear space $\Phi$. This is the enveloping algebra of
the abelian Lie group of translations in $\Phi$. The generating functions of
unitary representations of this group play the role of Euclidean generating
functionals in algebraic QFT. They are the Fourier transforms of measures in
the dual $\Phi'$ to the space $\Phi$. By analogy with the case of boson fields,
the corresponding anticommutative algebra of fermion fields is defined to be
the algebra of functions taking their values into an infinite Grassman algebra.
