  An L-embedded Banach spaace is a Banach space which is complemented in its
bidual such that the norm is additive between the two complementary parts. On
such spaces we define a topology, called an abstract measure topology, which by
known results coincides with the usual measure topology on preduals of finite
von Neumann algebras (like $L_1([0,1])$). Though not numerous, the known
properties of this topology suffice to generalize several results on subspaces
of $L_1([0,1])$ to subspaces of arbitrary L-embedded spaces.
