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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A density property and applications


Author: Richard J. O’Malley
Journal: Trans. Amer. Math. Soc. 199 (1974), 75-87
MSC: Primary 26A48
DOI: https://doi.org/10.1090/S0002-9947-1974-0360955-X
MathSciNet review: 0360955
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Abstract: An unexpected metric density property of a certain type of $ {F_\sigma }$ set is proven. An immediate application is a characterization of monotone functions similar to a well-known result by Zygmund. Several corollaries of this characterization are given as well as a simple proof of a theorem due to Tolstoff.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0360955-X
Article copyright: © Copyright 1974 American Mathematical Society