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The Quarterly Journal of Mathematics Advance Access originally published online on July 18, 2006
The Quarterly Journal of Mathematics 2007 58(1):71-79; doi:10.1093/qmath/hal011
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© 2006. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

GENERATING SEQUENCES OF FUNCTIONS

J. D. Mitchell{dagger}, Y. Péresse and M. R. Quick

Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9SS, Scotland

{dagger} Corresponding author. E-mail: jdm3{at}st-and.ac.uk

Received 3 January 2006; revised 8 June 2006
  Abstract

We consider the problem of obtaining an arbitrary countable collection of functions with specific properties as a composition of finitely many functions with the same property. The functions investigated are continuous, Baire-n, Lebesgue or Borel measurable, increasing, and differentiable functions on [0, 1], and increasing functions on N.


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