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

 

On the Denjoy rank, the Kechris-Woodin rank and the Zalcwasser rank


Author: Haseo Ki
Journal: Trans. Amer. Math. Soc. 349 (1997), 2845-2870
MSC (1991): Primary 04A15, 26A21; Secondary 42A20
MathSciNet review: 1390042
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Abstract: We show that the Denjoy rank and the Zalcwasser rank are incomparable. We construct for any countable ordinal $\alpha $ differentiable functions $f$ and $g$ such that the Zalcwasser rank and the Kechris-Woodin rank of $f$ are $\alpha +1$ but the Denjoy rank of $f$ is 2 and the Denjoy rank and the Kechris-Woodin rank of $g$ are $\alpha +1$ but the Zalcwasser rank of $g$ is 1. We then derive a theorem that shows the surprising behavior of the Denjoy rank, the Kechris-Woodin rank and the Zalcwasser rank.


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Additional Information

Haseo Ki
Affiliation: Department of Mathematics, Yonsei University, Seoul, 120-749, Korea
Email: haseo@bubble.yonsei.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01767-4
PII: S 0002-9947(97)01767-4
Keywords: Denjoy rank, descriptive set theory, Fourier series, Kechris-Woodin rank, Zalcwasser rank
Received by editor(s): April 13, 1995
Received by editor(s) in revised form: January 18, 1996
Additional Notes: Partially supported by GARC-KOSEF
Article copyright: © Copyright 1997 American Mathematical Society