# 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

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topDarji, 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

top- [1] U. B. Darji and M. J. Evans, Recovering Baire one functions, Mathematika 42 (1995), 43-48. Zbl0822.54012
- [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] 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] 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] 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] 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] S. Kempisty, Sur les fonctions quasicontinues, Fund. Math. 19 (1932), 184-197. Zbl58.0246.01
- [8] K. Kuratowski, Topology, Vol. I, Academic Press, 1966.
- [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] D. Preiss, Maximoff's theorem, Real Anal. Exchange 5 (1979), 92-104.

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