  We describe a necessary and sufficient condition for the convergence to
minimum Bayes risk when training two-layer ReLU-networks by gradient descent in
the mean field regime with omni-directional initial parameter distribution.
This article extends recent results of Chizat and Bach to ReLU-activated
networks and to the situation in which there are no parameters which exactly
achieve MBR. The condition does not depend on the initalization of parameters
and concerns only the weak convergence of the realization of the neural
network, not its parameter distribution.
