  The notion of direct integrals introduced by Haydon, Levy and Raynaud in 1991
is a generalisation of the well-known concept of K\"othe-Bochner spaces of
vector-valued functions (using a family of target spaces instead of just one
space). Here we will discuss some classical geometric properties like strict
convexity, local uniform convexity and uniform convexity in direct integrals.
We will also consider strongly convex and very convex K\"othe-Bochner spaces.
