Abstract

The pointwise limit S of a sequence of Stieltjes transforms (Sn) of real Borel probability measures (Pn) is itself the Stieltjes transform of a Borel p.m. P if and only if iy S(iy) →−1as y →∞, in which case Pn converges to P in distribution. Applications are given to several problems in mathematical physics.

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Mathematics

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Mathematics Commons

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URL: http://digitalcommons.calpoly.edu/rgp_rsr/9