Kechris, A. S. and Louveau, A. (1990) A Classification of Baire Class 1 Functions. Transactions of the American Mathematical Society, 318 (1). pp. 209-236. ISSN 0002-9947. https://resolver.caltech.edu/CaltechAUTHORS:20130522-151355415
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Abstract
We study in this paper various ordinal ranks of (bounded) Baire class 1 functions and we show their essential equivalence. This leads to a natural classification of the class of bounded Baire class 1 functions B_1 in a transfinite hierarchy B^ξ_1 ξ < ω_1) of "small" Baire classes, for which (for example) an analysis similar to the Hausdorff-Kuratowski analysis of Δ^0_2 sets via transfinite differences of closed sets can be carried out. The notions of pseudouniform convergence of a sequence of functions and optimal convergence of a sequence of continuous functions to a Baire class 1 function ƒ are introduced and used in this study.
| Item Type: | Article | |||||||||
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| Additional Information: | © 1990 American Mathematical Society. Received by the editors December 15, 1987 and, in revised form, June 3, 1988. Research of the first author was partially supported by NSF Grant DMS-8718847. | |||||||||
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| Issue or Number: | 1 | |||||||||
| Classification Code: | 1980 Mathematics Subject Classification (1985 Revision). Primary 03E15, 04A15, 46B99 | |||||||||
| Record Number: | CaltechAUTHORS:20130522-151355415 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20130522-151355415 | |||||||||
| Official Citation: | A classification of Baire class 1 functions A. S. Kechris and A. Louveau. Trans. Amer. Math. Soc. 318 (1990), 209-236 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 38639 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 22 May 2013 22:33 | |||||||||
| Last Modified: | 03 Oct 2019 04:59 |
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