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Structure of the set of continuous functions with Luzin’s property (N). (English) Zbl 0968.26008

The authors proved that the set of all continuous mappings of \([0,1]^n\) to \(R^n\) with Luzin’s property (N) with respect to the Lebesgue measure is a coanalytic non-Borel and first category subset of the space of all continuous mappings.

MSC:

26B35 Special properties of functions of several variables, Hölder conditions, etc.
54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
26B05 Continuity and differentiation questions
26A30 Singular functions, Cantor functions, functions with other special properties
28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
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