Fine properties of Baire one functions

Udayan Darji; Michael Evans; Chris Freiling; Richard O'Malley

Fundamenta Mathematicae (1998)

  • Volume: 155, Issue: 2, page 177-188
  • ISSN: 0016-2736

Abstract

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A new theorem in the theory of first return representations of Baire class one functions of a real variable is presented which has as immediate consequences several known characterizations of standard subclasses of the Baire one functions. Further, this theorem yields new insights into how finely Baire one functions can be recovered and yields a characterization of another subclass of Baire one functions.

How to cite

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Darji, Udayan, et al. "Fine properties of Baire one functions." Fundamenta Mathematicae 155.2 (1998): 177-188. <http://eudml.org/doc/212250>.

@article{Darji1998,
abstract = {A new theorem in the theory of first return representations of Baire class one functions of a real variable is presented which has as immediate consequences several known characterizations of standard subclasses of the Baire one functions. Further, this theorem yields new insights into how finely Baire one functions can be recovered and yields a characterization of another subclass of Baire one functions.},
author = {Darji, Udayan, Evans, Michael, Freiling, Chris, O'Malley, Richard},
journal = {Fundamenta Mathematicae},
keywords = {first return representations of Baire class one functions},
language = {eng},
number = {2},
pages = {177-188},
title = {Fine properties of Baire one functions},
url = {http://eudml.org/doc/212250},
volume = {155},
year = {1998},
}

TY - JOUR
AU - Darji, Udayan
AU - Evans, Michael
AU - Freiling, Chris
AU - O'Malley, Richard
TI - Fine properties of Baire one functions
JO - Fundamenta Mathematicae
PY - 1998
VL - 155
IS - 2
SP - 177
EP - 188
AB - A new theorem in the theory of first return representations of Baire class one functions of a real variable is presented which has as immediate consequences several known characterizations of standard subclasses of the Baire one functions. Further, this theorem yields new insights into how finely Baire one functions can be recovered and yields a characterization of another subclass of Baire one functions.
LA - eng
KW - first return representations of Baire class one functions
UR - http://eudml.org/doc/212250
ER -

References

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  1. [1] U. B. Darji and M. J. Evans, Recovering Baire one functions, Mathematika 42 (1995), 43-48. Zbl0822.54012
  2. [2] U. B. Darji, M. J. Evans, and P. D. Humke, First return approachability, J. Math. Anal. Appl. 199 (1996), 545-557. Zbl0854.26001
  3. [3] U. B. Darji, M. J. Evans, and R. J. O'Malley, First return path systems: differentiability, continuity, and orderings, Acta Math. Hungar. 66 (1995), 83-103. Zbl0821.26006
  4. [4] U. B. Darji, M. J. Evans, and R. J. O'Malley, A first return characterization of Baire one functions, Real Anal. Exchange 19 (1993-94), 510-515. Zbl0840.26005
  5. [5] U. B. Darji, M. J. Evans, and R. J. O'Malley, Universally first return continuous functions, Proc. Amer. Math. Soc. 123 (1995), 2677-2685. Zbl0846.26003
  6. [6] M. J. Evans and R. J. O'Malley, Fine tuning the recoverability of Baire one functions, Real Anal. Exchange 21 (1995-96), 165-174. 
  7. [7] S. Kempisty, Sur les fonctions quasicontinues, Fund. Math. 19 (1932), 184-197. Zbl58.0246.01
  8. [8] K. Kuratowski, Topology, Vol. I, Academic Press, 1966. 
  9. [9] I. Maximoff, Sur la transformation continue de quelques fonctions en dérivées exactes, Bull. Soc. Phys. Math. Kazan (3) 12 (1940), 57-81. Zbl0063.03850
  10. [10] D. Preiss, Maximoff's theorem, Real Anal. Exchange 5 (1979), 92-104. 

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