Distribution (mathematics) - Localization of Distributions

Localization of Distributions

There is no way to define the value of a distribution in D'(U) at a particular point of U. However, as is the case with functions, distributions on U restrict to give distributions on open subsets of U. Furthermore, distributions are locally determined in the sense that a distribution on all of U can be assembled from a distribution on an open cover of U satisfying some compatibility conditions on the overlap. Such a structure is known as a sheaf.