  We study and characterize stability, NIP and NSOP in terms of topological and
measure theoretical properties of classes of functions. We study a measure
theoretic property, `Talagrand's stability', and explain the relationship
between this property and NIP in continuous logic. Using a result of Bourgain,
Fremlin and Talagrand, we prove the `almost definability' and `Baire~1
definability' of coheirs assuming NIP. We show that a formula $\phi(x,y)$ has
the strict order property if and only if there is a convergent sequence of
continuous functions on the space of $\phi$-types such that its limit is not
continuous. We deduce from this a theorem of Shelah and point out the
correspondence between this theorem and the Eberlein-\v{S}mulian theorem.
