TYPICAL MEASURABLE FUNCTION IN THE TOPOLOGY OF CLOSE APPROXIMATION
J. TISER and L. ZAJICEK
Abstract.
We show 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 non empty 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.
Compressed Postscript 
