Real Analysis Exchange

A New Proof of a Theorem of Jayne and Rogers

Luca Motto Ros and Brian Semmes

Full-text: Open access


We give a new simpler proof of a theorem of Jayne and Rogers.

Article information

Real Anal. Exchange, Volume 35, Number 1 (2009), 195-204.

First available in Project Euclid: 27 April 2010

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03E15: Descriptive set theory [See also 28A05, 54H05] 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05]

Baire class 1 functions piecewise continuous functions first level Borel functions $\bDelta^0_2$-functions


Ros, Luca Motto; Semmes, Brian. A New Proof of a Theorem of Jayne and Rogers. Real Anal. Exchange 35 (2009), no. 1, 195--204.

Export citation


  • R. Engelking, General topology, Sigma Series in Pure Mathematics 6, Heldermann Verlag, Berlin, 1989.
  • R. W. Hansell, On Borel mappings and Baire functions, Trans. Amer. Math. Soc. 194 (1974), 195–211.
  • P. Holický, L. Zajíček and M. Zelený, A remark on a theorem of Solecki, Comment. Math. Univ. Carolin. 46 (2005), 43–54.
  • J. E. Jayne and C. A. Rogers, First level Borel functions and isomorphisms, J. Math. Pures Appl. 61 (1982), 177–205.
  • A. S. Kechris, Classical descriptive set theory, Graduate Text in Mathematics, no. 156, Springer-Verlag, Heidelberg, New York, 1995.
  • S. Solecki, Decomposing Borel sets and functions and the structure of Baire class 1 functions, J. Amer. Math. Soc. 11(3) (1998), 521–550.