Functions Equivalent to Borel Measurable Ones
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.