Existence for stochastic 2D Euler equations with positive $H^{-1}$ vorticity

We prove the existence of non-negative measure- and $H^{-1}$-valued vorticity solutions to the stochastic 2D Euler equations with transport vorticity noise, starting from any non-negative vortex sheet. This extends the result by Delort (J.Amer.Math.Soc. 1991) to the stochastic case.