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# Sets on which measurable functions are determined by their range

Published:1997-12-01
Printed: Dec 1997
• Maxim R. Burke
• Krzysztof Ciesielski
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## Abstract

We study sets on which measurable real-valued functions on a measurable space with negligibles are determined by their range.
 Keywords: measurable function, measurable space with negligibles, continuous image, set of range uniqueness (SRU)
 MSC Classifications: 28A20 - Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence 28A05 - Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05] 54C05 - Continuous maps 26A30 - Singular functions, Cantor functions, functions with other special properties 03E35 - Consistency and independence results 03E50 - Continuum hypothesis and Martin's axiom [See also 03E57]

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