  Linear second order elliptic boundary value problems (BVP) on bounded
Lipschitz domains are studied in the case of Gaussian white noise loads.
Especially, Neumann and Robin BVPs are considered.
  The main obstacle for applying the usual variational approach is that the
Gaussian white noise has irregular realizations. In particular, the
corresponding Neumann boundary values are not well-defined in the ordinary
sense.
  In this work, the BVP is reformulated by replacing the continuity of the
boundary trace mapping with measurability. Instead of using variational methods
alone, the reformulation of the BVP derives also from Cameron-Martin space
techniques. The reformulation essentially returns the study of irregular white
noise loads to study of $L^2$-loads.
  Admissibility of the reformulation is demonstrated by showing that usual
finite element approximations of the BVP with discretized white noise loads
converge to the solution of the reformulated problem. For Neumann and Robin
BVPs, the finite dimensional approximations have been utilized before. However,
here also the infinite-dimensional limit is considered.
