We show that the Calabi homomorphism extends to some groups of homeomorphisms on exact symplectic manifolds. The proof is based on the uniqueness of the generating Hamiltonian (proved by Viterbo) of continuous Hamiltonian isotopies (introduced by Oh and Muller).
"The Calabi invariant for some groups of homeomorphisms." J. Symplectic Geom. 9 (1) 107 - 117, March 2011.