Coordinatewise decomposition of group-valued Borel functions
Volume 196 / 2007
Fundamenta Mathematicae 196 (2007), 119-126
MSC: Primary 03E15; Secondary 28A05.
DOI: 10.4064/fm196-2-2
Abstract
Answering a question of Kłopotowski, Nadkarni, Sarbadhikari, and Srivastava, we characterize the Borel sets $S \subseteq X \times Y$ with the property that every Borel function $f : S \rightarrow \mathbb C$ is of the form $f(x,y) = u(x) + v(y)$, where $u : X \rightarrow \mathbb C$ and $v : Y \rightarrow \mathbb C$ are Borel.
