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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Sets of multiplicity and differentiable functions. II


Author: Robert Kaufman
Journal: Trans. Amer. Math. Soc. 200 (1974), 427-435
MSC: Primary 42A72; Secondary 26A16
MathSciNet review: 0380258
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Abstract: The stability of certain sets of multiplicity is studied with reference to special classes of differentiable functions. Kronecker sets are produced as examples of instability. The most difficult theorem uses probability theory and an estimation of Kolmogoroff's $ \varepsilon $-entropy in a certain space of functions.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0380258-7
PII: S 0002-9947(1974)0380258-7
Keywords: Kronecker set, $ {M_0}$-set, $ {C^1}$ function, Riemann-Lebesgue lemma
Article copyright: © Copyright 1974 American Mathematical Society