  This paper is concerned with dynamic user equilibrium (DUE) with elastic
travel demand (E-DUE). We present and prove a variational inequality (VI)
formulation of E-DUE using measure-theoretic argument. Moreover, existence of
the E-DUE is formally established with a version of Brouwer's fixed point
theorem in a properly defined Hilbert space. The existence proof requires the
effective delay operator to be continuous, a regularity condition also needed
to ensure the existence of DUE with fixed demand (Han et al., 2013c). Our proof
does not invoke the a priori upper bound of the departure rates (path flows).
