In this note, we consider Keisler's stability theory and prove that every measure over a small submodel has a locally pure extension.

We study conditions for structures based on Banach spaces having the property that each set definable by neocompact formula is equivalent to the countable intersection of sets definable by quantifier-free formulas. We show that this property is invariant with respect to different nonstandard hull constructions and it is the same as Henson's Quantifier Elimination in sufficiently saturated nonstandard hulls of internal Banach spaces.