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Construction of a function which is continuous from \([0,1]\) into certain Banach spaces and non-measurable from \([0,1]\) into another space with some more strong topology. (Construction d’une fonction \(f\) continue de \([0,1]\) dans certains espaces de Banach et non mesurable de \([0,1]\) dans un autre, de topologie légèrement plus forte.) (French) Zbl 0972.28001

Summary: The purpose of this note is to construct a non-measurable function \(f\) defined on \([0,1]\) with values in the Hölder space \(C^r(\mathbb{R})\) \((r\in ]0,1[)\) which, as a function with values in any space \(C^{r'}(\mathbb{R})\) \((r'< r)\), is continuous.

MSC:

28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
35Q30 Navier-Stokes equations
40A30 Convergence and divergence of series and sequences of functions
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