We prove the existence and uniqueness of probabilistically strong solutions
to stochastic porous media equations driven by time-dependent multiplicative
noise on a general measure space (E,B(E),μ), and the Laplacian
replaced by a self-adjoint operator L. In the case of Lipschitz
nonlinearities Ψ, we in particular generalize previous results for open
E⊂Rd and L=Laplacian to fractional Laplacians. We also
generalize known results on general measure spaces, where we succeeded in
dropping the transience assumption on L, in extending the set of allowed
initial data and in avoiding the restriction to superlinear behavior of Ψ
at infinity for L2(μ)-initial data.Comment: 18page