This talk is concerned with the theoretical understanding of alpha-stable sheets X. Our motivation for this is in the context of Bayesian inverse problems, where we consider the treatment of these processes as prior forms for parameter estimation. We derive various convergence results of these processes. In doing so we use a number of variants which these sheets can take, such as a stochastic integral representation, but also random series expansions through Poisson processes. Our convergence analysis will rely on the fact of whether X omits sample paths, and if so how regular the paths are. Time permitted we will discuss well-posedness of the inverse problem.