In this book we do not need to use the Levy continuity theorem, cf. Feller (1966). For the uses illustrated below inversion theorems for the various transforms are sufficient. Inversion of Fourier transforms has been rendered almost trivial by the elegant calculation that appears in Feller, op. cit. Multidimensional uniqueness theorems for the (complex) Laplace transform are proven easily by induction on the dimension and these proofs are stated in the sequel. For more detail than is presented in this chapter suitable references are Feller (1966), Widder (1941) and Wiener (1933).
KeywordsDensity Function Uniqueness Theorem Borel Subset Noncentrality Parameter Inversion Theorem
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