TY - JOUR AU - Izzo, Alexander J. PY - 2016/06/09 Y2 - 2024/03/29 TI - Existence of Continuous Functions That Are One-to-One Almost Everywhere JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 118 IS - 2 SE - Articles DO - 10.7146/math.scand.a-23688 UR - https://www.mscand.dk/article/view/23688 SP - 269-276 AB - It is shown that given a metric space $X$ and a $\sigma$-finite positive regular Borel measure $\mu$ on $X$, there exists a bounded continuous real-valued function on $X$ that is one-to-one on the complement of a set of $\mu$ measure zero. ER -