＜正＞ Let X=Rd（d＞1）.Consider the unitary representations of Diff（X）given by quasi-invariant measures under the action of Diff（X）.The author proposes smooth point measuresas generalization of Poisson point measures and proves that every smooth point measure isquasi-invariant under the action of Diff（X）and if {Ugi},i=1,2,are the unitary represen-tations of Diff（X）given by the smooth point measures μi,i=1,2,respectively,then {Ug~1}is unitarily equivalent to {Ug~2} iff μ1 is equivalent to μ2 as measure.
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