Existence of Continuous Functions That Are One-to-One Almost Everywhere

• Autores: Alexander J. Izzo
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 118, Nº 2, 2016, págs. 269-276
• Idioma: inglés
• DOI: 10.7146/math.scand.a-23688
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• Resumen

  • 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.