  This paper is a modified chapter of the author's Ph.D. thesis. We introduce
the notions of sequentially approximated types and sequentially approximated
Keisler measures. As the names imply, these are types which can be approximated
by a sequence of realized types and measures which can be approximated by a
sequence of "averaging measures" on tuples of realized types. We show that both
generically stable types (in arbitrary theories) and Keisler measures which are
finitely satisfiable over a countable model (in NIP theories) are sequentially
approximated. We also introduce the notion of a smooth sequence in a measure
over a model and give an equivalent characterization of generically stable
measures (in NIP theories) via this definition.
