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In this paper sufficient conditions are given in order that every distribution invariant under a Lie group extend from the set of orbits of maximal dimension to the whole of the space. It is shown that these conditions are satisfied for the n-point action of the pure Lorentz group and for a standard action of the Lorentz group of arbitrary signature. 2000 Mathematics Subject Classification: Primary 46F10; Secondary 22F05, 22E99.doi:10.4064/ap-74-1-13-25 fatcat:qiii5a4jkraxhibmmcjmowtwwu