Functions Equivalent to Borel Measurable Ones

Volume 58 / 2010

Andrzej Komisarski, Henryk Michalewski, Pawe/l Milewski Bulletin Polish Acad. Sci. Math. 58 (2010), 55-64 MSC: Primary 54H05; Secondary 03E15, 54C10. DOI: 10.4064/ba58-1-7

Abstract

Let $X$ and $Y$ be two Polish spaces. Functions $f,g:X\to Y$ are called equivalent if there exists a bijection $\varphi$ from $X$ onto itself such that $g\circ\varphi=f$. Using a theorem of J. Saint Raymond we characterize functions equivalent to Borel measurable ones. This characterization answers a question asked by M. Morayne and C. Ryll-Nardzewski.

Authors

  • Andrzej KomisarskiInstitute of Mathematics
    University of /Lódź
    Banacha 22
    90-238 /Lódź, Poland
    e-mail
  • Henryk MichalewskiInstitute of Mathematics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland
    e-mail
  • Pawe/l MilewskiInstitute of Mathematics
    University of Warsaw
    Banacha 2
    02–097 Warszawa, Poland
    e-mail

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