Functions Equivalent to Borel Measurable Ones
Volume 58 / 2010
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.
