Pseudofinite groups and VC-dimension

We develop "local NIP group theory" in the context of pseudofinite groups. In particular, given a sufficiently saturated pseudofinite structure G expanding a group, and left invariant NIP formula delta(x; (y) over bar), we prove various aspects of "local fsg" for the right-stratified formula delta(r) (x; (y) over bar, u) := delta(x . u; (y) over bar). This includes a delta(r)-type-definable connected component, uniqueness of the pseudofinite counting measure as a left-invariant measure on delta(r)-formulas and generic compact domination for delta(r)-definable sets.