Geodesic
TYPICAL MEASURABLE FUNCTION IN THE TOPOLOGY OF CLOSE APPROXIMATION
Acta mathematica Universitatis Comenianae, Tome 60 (1991) no. 1 
J. Tiser; L. Zajicek. TYPICAL MEASURABLE FUNCTION IN THE TOPOLOGY OF CLOSE APPROXIMATION. Acta mathematica Universitatis Comenianae, Tome 60 (1991) no. 1. http://geodesic.mathdoc.fr/item/AMUC_1991_60_1_a4/
@article{AMUC_1991_60_1_a4,
     author = {J. Tiser and L. Zajicek},
     title = {TYPICAL {MEASURABLE} {FUNCTION} {IN} {THE} {TOPOLOGY} {OF} {CLOSE} {APPROXIMATION}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {1991},
     volume = {60},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_1991_60_1_a4/}
}
TY  - JOUR
AU  - J. Tiser
AU  - L. Zajicek
TI  - TYPICAL MEASURABLE FUNCTION IN THE TOPOLOGY OF CLOSE APPROXIMATION
JO  - Acta mathematica Universitatis Comenianae
PY  - 1991
VL  - 60
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/AMUC_1991_60_1_a4/
ID  - AMUC_1991_60_1_a4
ER  - 
%0 Journal Article
%A J. Tiser
%A L. Zajicek
%T TYPICAL MEASURABLE FUNCTION IN THE TOPOLOGY OF CLOSE APPROXIMATION
%J Acta mathematica Universitatis Comenianae
%D 1991
%V 60
%N 1
%U http://geodesic.mathdoc.fr/item/AMUC_1991_60_1_a4/
%F AMUC_1991_60_1_a4

Voir la notice de l'article provenant de la source Comenius University

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.