  The purpose of this paper is to define for every Polish space $X$ a class of
sets, the $EBP(X)$-sets or the extended Baire property sets, to work out many
properties of the $EBP(X)$-sets and to show their usefulness in analysis. For
example, a proper generalization of the Pettis Theorem is proved in this
context that furnishes a new automatic continuity result for Polish groups. The
name extended Baire property sets is reasonable since $EBP(X)$ contains the
Baire property sets $BP(X)$ and it is consistent with ZFC that the containment
is proper.
