The autocontinuity of set function and the fuzzy integral

AbstractThe autocontinuity and some other concepts of a set function are introduced and Sugeno's fuzzy measure with some annexed conditions is studied. On a fuzzy measure space, Egoroffs theorem is proved. It is also proved that F-mean convergence is equivalent to convergence in measure for a sequence of measurable functions. Finally, some convergence theorems of sequence of fuzzy integrals are proved, especially, using the concept of autocontinuity, a necessary and sufficient condition for the convergence in measure theorem is given