# Continuous-, derivative-, and differentiable-restrictions of measurable functions

Fundamenta Mathematicae (1992)

- Volume: 141, Issue: 1, page 85-95
- ISSN: 0016-2736

## Access Full Article

top## Abstract

top## How to cite

topBrown, Jack. "Continuous-, derivative-, and differentiable-restrictions of measurable functions." Fundamenta Mathematicae 141.1 (1992): 85-95. <http://eudml.org/doc/211953>.

@article{Brown1992,

abstract = {We review the known facts and establish some new results concerning continuous-restrictions, derivative-restrictions, and differentiable-restrictions of Lebesgue measurable, universally measurable, and Marczewski measurable functions, as well as functions which have the Baire properties in the wide and restricted senses. We also discuss some known examples and present a number of new examples to show that the theorems are sharp.},

author = {Brown, Jack},

journal = {Fundamenta Mathematicae},

keywords = {Lebesgue measurability; Marczewski measurability; universally measurable sets; continuous-restrictions; derivative-restrictions; Baire properties},

language = {eng},

number = {1},

pages = {85-95},

title = {Continuous-, derivative-, and differentiable-restrictions of measurable functions},

url = {http://eudml.org/doc/211953},

volume = {141},

year = {1992},

}

TY - JOUR

AU - Brown, Jack

TI - Continuous-, derivative-, and differentiable-restrictions of measurable functions

JO - Fundamenta Mathematicae

PY - 1992

VL - 141

IS - 1

SP - 85

EP - 95

AB - We review the known facts and establish some new results concerning continuous-restrictions, derivative-restrictions, and differentiable-restrictions of Lebesgue measurable, universally measurable, and Marczewski measurable functions, as well as functions which have the Baire properties in the wide and restricted senses. We also discuss some known examples and present a number of new examples to show that the theorems are sharp.

LA - eng

KW - Lebesgue measurability; Marczewski measurability; universally measurable sets; continuous-restrictions; derivative-restrictions; Baire properties

UR - http://eudml.org/doc/211953

ER -

## References

top- [1] S. Agronsky, A. M. Bruckner, M. Laczkovich and D. Preiss, Convexity conditions and intersections with smooth functions, Trans. Amer. Math. Soc. 289 (1985), 659-677. Zbl0601.26007
- [2] H. Blumberg, New properties of all real functions, ibid. 24 (1922), 113-128.
- [3] J. B. Brown, Differentiable restrictions of real functions, Proc. Amer. Math. Soc. 108 (1990), 391-398. Zbl0692.26002
- [4] J. B. Brown and K. Prikry, Variations on Lusin's theorem, Trans. Amer. Math. Soc. 302 (1987), 77-86. Zbl0619.28005
- [5] A. M. Bruckner, J. G. Ceder and M. L. Weiss, On the differentiability structure of real functions, ibid. 142 (1969), 1-13. Zbl0182.38301
- [6] J. Ceder, Some examples on continuous restrictions, Real Anal. Exchange 7 (1981/ 82), 155-162. Zbl0533.26002
- [7] F. Filipczak, Sur les fonctions continues relativement monotones, Fund. Math. 58 (1966), 75-87. Zbl0185.12204
- [8] V. Jarník, Sur les nombres dérivés approximatifs, ibid. 22 (1934), 4-16.
- [9] C. Kuratowski, La propriété de Baire dans les espaces métriques, ibid. 16 (1930), 390-394. Zbl56.0846.03
- [10] K. Kuratowski and A. Mostowski, Set Theory with an Introduction to Descriptive Set Theory, North-Holland, Amsterdam 1976. Zbl0337.02034
- [11] M. Laczkovich, Differentiable restrictions of continuous functions, Acta Math. Hungar. 44 (1984), 355-360. Zbl0558.26005
- [12] N. Lusin, Sur les propriétés des fonctions mesurables, C. R. Acad. Sci. Paris 154 (1912), 1688-1690. Zbl43.0484.04
- [13] N. Lusin, Sur la recherche des fonctions primitives, ibid. 162 (1916), 975-978. Zbl46.0390.02
- [14] E. Marczewski (Szpilrajn), Sur une classe de fonctions de M. Sierpiński et la classe correspondante d'ensembles, Fund. Math. 24 (1935), 17-34. Zbl61.0229.01

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.