  The group Hameo (M,\omega) of Hamiltonian homeomorphisms of a connected
symplectic manifold (M,\omega) was defined and studied in [7] and further in
[6]. In these papers, the authors consistently used the L^{(1,\infty)}-Hofer
norm (and not the L^\infty-Hofer norm) on the space of Hamiltonian paths (see
below for the definitions). A justification for this choice was given in [7].
In this article we study the L^\infty-case. In view of the fact that the Hofer
norm on the group Ham (M,\omega) of Hamiltonian diffeomorphisms does not depend
on the choice of the L^{(1,\infty)}-norm vs. the L^\infty-norm [9], Y.-G. Oh
and D. McDuff (private communications) asked whether the two notions of
Hamiltonian homeomorphisms arising from the different norms coincide. We will
give an affirmative answer to this question in this paper.
