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A Necessary and Sufficient Condition for the Existence of a Stieltjes Integral

โœ Scribed by Gilbert Ames Bliss


Book ID
123664837
Publisher
National Academy of Sciences
Year
1917
Tongue
English
Weight
227 KB
Volume
3
Category
Article
ISSN
0027-8424

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Necessary and sufficient condition that
โœ Jeffrey S. Geronimo; Theodore P. Hill ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 144 KB

The pointwise limit S of a sequence of Stieltjes transforms รฐS n รž of real Borel probability measures รฐP n รž is itself the Stieltjes transform of a Borel p.m. P if and only if iySรฐiyรž-ร€ 1 as y-N; in which case P n converges to P in distribution. Applications are given to several problems in mathemat