Topological duals of locally convex function spaces

Abstract This paper studies topological duals of locally convex function spaces that are natural generalizations Fréchet and Banach spaces. The dual is identified with the direct sum another space, a space purely finitely additive measures annihilator $$L^\infty $$ L ? . allows for quick proofs various classical as well new duality results e.g. in Lebesgue, Musielak–Orlicz, Orlicz–Lorentz associated risk measures. Beyond spaces, we obtain completeness general paired random variables.