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Sets on which measurable functions are determined by their range

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Published:1997-12-01
Printed: Dec 1997

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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) measurable function, measurable space with negligibles, continuous image, set of range uniqueness (SRU)

MSC Classifications:

28A20, 28A05, 54C05, 26A30, 03E35, 03E50 show english descriptions Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]
Continuous maps
Singular functions, Cantor functions, functions with other special properties
Consistency and independence results
Continuum hypothesis and Martin's axiom [See also 03E57] 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]