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Typical measurable function in the topology of close approximation. (English) Zbl 0733.28001

Author’ abstract: It is shown that the typical Lebesgue or Baire measurable function with respect to the topology of close approximation has the range of second category and that there are nonempty open sets of the space of measurable functions where the typical function has \(G_{\delta}\) dense range and the preimage of every point of the range contains a perfect set.

MSC:

28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
26A99 Functions of one variable
54C30 Real-valued functions in general topology
54C35 Function spaces in general topology
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