  Dalitz decays of $\omega$ and $\rho$ mesons, $\omega\to \pi^0\gamma^*\to\pi^0
e^+e^-$ and $\rho^0\to \pi^0\gamma^*\to\pi^0 e^+e^-$, produced in $pp$
collisions are calculated within a covariant effective meson-nucleon theory. We
argue that the $\omega$ transition form factor $F_{\omega\to \pi^0\gamma^*}$ is
experimentally accessible in a fairly model independent way in the reaction $pp
\to pp \pi^0 e^+ e^-$ for invariant masses of the $\pi^0 e^+ e^-$ subsystem
near the $\omega$ pole. Numerical results are presented for the intermediate
energy kinematics of envisaged HADES experiments.
