Algebras of Borel measurable functions

Michał Morayne

Fundamenta Mathematicae (1992)

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

Abstract

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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.

How to cite

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Morayne, 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

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

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