On the class of distributions compatible with locality

An investigation is made of the question of the largest class of distributions that admits a formulation of microcausality. To this end a study is made of the local properties of functionals over quasianalytic classes. Such functionals are shown to allow a natural generalization of the notion of concentration on a fixed set. It is shown that, in contrast to the usual case of test-function spaces of ftmctions with compact support, the limit of a sequence of functionals that are concentrated on a fixed set need not be concentrated on this set.