Geodesic
Functions Equivalent to Borel Measurable Ones
Andrzej Komisarski 1   ; Henryk Michalewski 2   ; Paweł Milewski 3
1 Institute of Mathematics University of Łódź Banacha 22 90-238 Łódź, Poland
2 Institute of Mathematics University of Warsaw Banacha 2 02-097 Warszawa, Poland
3 Institute of Mathematics University of Warsaw Banacha 2 02–097 Warszawa, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) no. 1, pp. 55-64 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ba58-1-7
Keywords: polish spaces functions called equivalent there exists nbsp bijection varphi nbsp itself circ varphi using theorem nbsp saint raymond characterize functions equivalent borel measurable characterization answers question asked nbsp morayne nbsp ryll nardzewski

Andrzej Komisarski  1   ; Henryk Michalewski  2   ; Paweł Milewski  3

1 Institute of Mathematics University of Łódź Banacha 22 90-238 Łódź, Poland
2 Institute of Mathematics University of Warsaw Banacha 2 02-097 Warszawa, Poland
3 Institute of Mathematics University of Warsaw Banacha 2 02–097 Warszawa, Poland 
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Andrzej Komisarski; Henryk Michalewski; Paweł  Milewski. Functions Equivalent to Borel Measurable Ones. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) no. 1, pp. 55-64. doi: 10.4064/ba58-1-7

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