Is there a general theory of integration of functions with values in a topological vector space (not necessarily locally convex)?
Browsing through mathoverflow posts, I came across a discussion regarding Grothendieck's work on integration with values in a topological group L'intégration à valeurs dans un groupe topologique (Reference request : Grothendieck's topological space valued integral ). Unfortunately the requested reference is never provided. Does anyone know of a rough sketch of the approach used?
Just to emphasize, I am interested in a general theory and not in notions such as the Bochner integral, or Gelfand-Pettis integral which use local convexity of the topological vector space.