Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Identity for Two Integral Transforms Applied to the Uniqueness of a
  Distribution via its Laplace-Stieltjes Transform   It is well known that the Laplace-Stieltjes transform of a nonnegative random
variable (or random vector) uniquely determines its distribution function. We
extend this uniqueness theorem by using the Muntz-Szasz Theorem and the
identity for the Laplace-Stieltjes and Laplace-Carson transforms of a
distribution function. The latter appears for the first time to the best of our
knowledge. In particular, if X and Y are two nonnegative random variables with
joint distribution H, then H can be characterized by a suitable set of
countably many values of its bivariate Laplace-Stieltjes transform. The general
high-dimensional case is also investigated. Besides, Lerch's uniqueness theorem
for conventional Laplace transforms is extended as well. The identity can be
used to simplify the calculation of Laplace-Stieltjes transforms when the
underlying distributions have singular parts. Finally, some examples are given
to illustrate the characterization results via the uniqueness theorem.

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The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga