Mild solutions of SPDEs driven by Poisson noise in infinite dimensions and their dependence on initial conditions We investigate stochastic partial differential equations in an infinite dimensional Hilbert space H of the following form: dX(t)=[AX(t)+F(X(t))]dt+B(X(t) y)q(dt dy) X(0)=g where q(dt dy) is a compensated Poisson random measure associated to a stationary Poisson point process on a [sigma] finite measure space (U C m) A is the generator of a strongly continuous semigroup F is a measurable mapping from H to H B is a measurable mapping from the product space HxU to H and g is an H valued random variable. We are interested in the existence and uniqueness of a so called mild solution. But apart from the existence and uniqueness of mild solutions our main interest is directed towards their regularity w.r.t. the initial datum g.Under Lipschitz assumptions on the drift and the diffusion we show that for every initial condition g which is a p integrable random variable there exists a unique mild solution in the space of predictable p integrable processes where p>=2. In the case that p equals two this is done by Banachs fixed point theorem and the help of the isometric property of the stochastic integral ...