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A Classification of Baire Class 1 Functions

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
Related URLs:
URLURL TypeDescription
http://www.ams.org/journals/tran/1990-318-01/S0002-9947-1990-0946424-3/PublisherUNSPECIFIED
http://www.jstor.org/stable/2001236PublisherUNSPECIFIED
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.
Funders:
Funding AgencyGrant Number
NSFDMS-8718847
Other Numbering System:
Other Numbering System NameOther Numbering System ID
MathSciNet ReviewMR0946424
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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