# Algebras of Borel measurable functions

Fundamenta Mathematicae (1992)

- Volume: 141, Issue: 3, page 229-242
- ISSN: 0016-2736

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topMorayne, Michał. "Algebras of Borel measurable functions." Fundamenta Mathematicae 141.3 (1992): 229-242. <http://eudml.org/doc/211962>.

@article{Morayne1992,

abstract = {We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.},

author = {Morayne, Michał},

journal = {Fundamenta Mathematicae},

keywords = {Baire classes; Borel measurable real functions; Polish space; Sierpiński classes},

language = {eng},

number = {3},

pages = {229-242},

title = {Algebras of Borel measurable functions},

url = {http://eudml.org/doc/211962},

volume = {141},

year = {1992},

}

TY - JOUR

AU - Morayne, Michał

TI - Algebras of Borel measurable functions

JO - Fundamenta Mathematicae

PY - 1992

VL - 141

IS - 3

SP - 229

EP - 242

AB - We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.

LA - eng

KW - Baire classes; Borel measurable real functions; Polish space; Sierpiński classes

UR - http://eudml.org/doc/211962

ER -

## References

top- [CM] J. Cichoń and M. Morayne, Universal functions and generalized classes of functions, Proc. Amer. Math. Soc. 102 (1988), 83-89. Zbl0646.26009
- [CMPS] J. Cichoń, M. Morayne, J. Pawlikowski and S. Solecki, Decomposing Baire functions, J. Symbolic Logic 56 (1991), 1273-1283. Zbl0742.04003
- [H] F. Hausdorff, Set Theory, Chelsea, New York 1962.
- [Ke] S. Kempisty, Sur les séries itérées des fonctions continues, Fund. Math. 2 (1921), 64-73. Zbl48.0276.04
- [Ku] K. Kuratowski, Topology I, Academic Press, New York 1966.
- [L] A. Lindenbaum, Sur les superpositions de fonctions represéntables analytiquement, Fund. Math. 23 (1934), 15-37; Corrections, ibid., 304. Zbl60.0195.02
- [Ma] R. D. Mauldin, On the Baire system generated by a linear lattice of functions, ibid. 68 (1970), 51-59.
- [Mo] Y. N. Moschovakis, Descriptive Set Theory, North-Holland, Amsterdam 1980.
- [S1] W. Sierpiński, Sur les fonctions développables en séries absolument convergentes de fonctions continues, Fund. Math. 2 (1921), 15-27. Zbl48.0276.01
- [S2] W. Sierpiński, Démonstration d'un théorème sur les fonctions de première classe, ibid., 37-40. Zbl48.0276.03

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