Sets which are dense in the space of all pettis integrable functions

Abstract

Using the examples given by S.J. Dilworth and M. Girardi, we prove that the set of all nowhere Pettis differentiable functions is a Gδ-dense set in the space of all X-valued Pettis integrable functions on [0, 1]. Also an another example of a dense set in the space of all Pettis integrable functions is given.

Quaestiones Mathematicae 23(2000), 525–528