CaltechAUTHORS
  A Caltech Library Service

Sets of everywhere singular functions

Kechris, Alexander S. (1985) Sets of everywhere singular functions. In: Recursion theory week. Lecture notes in mathematics. No.1141. Springer-Verlag , Berlin, pp. 233-244. ISBN 978-3-540-15673-4. https://resolver.caltech.edu/CaltechAUTHORS:20130528-102414726

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20130528-102414726

Abstract

In this paper we present a simple general method for demonstrating that in certain function spaces various sets consisting of functions that exhibit at every point a prescribed kind of singularity form a coanalytic but not Borel set. We illustrate this method by providing new proofs that the set of nowhere differential continuous functions on [0,1] is (coanalytic but) not Borel and similarly for the set of continuous functions on [0,1] which fail everywhere to have a unilateral derivative (including ± ∞) -- the so called Besicovitch functions. These results were originally proved by Mauldin, [Mau] and unpublished, respectively. We also give a new example of a coanalytic not Borel set, namely the set of integrable functions with everywhere divergent Fourier series. Finally, we formulate an abstract theorem, which includes as simple instances all the above and other similar examples.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/BFb0076223DOIUNSPECIFIED
Additional Information:© 1985 Springer-Verlag. Research partially supported by NSF Grant.
Funders:
Funding AgencyGrant Number
NSFUNSPECIFIED
Other Numbering System:
Other Numbering System NameOther Numbering System ID
MathSciNet ReviewMR0820783
Series Name:Lecture notes in mathematics
Issue or Number:1141
Record Number:CaltechAUTHORS:20130528-102414726
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130528-102414726
Official Citation:Kechris, A. (1985). Sets of everywhere singular functions. Recursion Theory Week. H.-D. Ebbinghaus, G. Müller and G. Sacks, Springer Berlin Heidelberg. 1141: 233-244.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38685
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:29 May 2013 17:18
Last Modified:03 Oct 2019 04:59

Repository Staff Only: item control page