  It is well known to generalize the meagre ideal replacing aleph_0 by a
(regular) cardinal lambda > aleph_0 and requiring the ideal to be
lambda^+-complete. But can we generalize the null ideal? In terms of forcing,
this means finding a forcing notion similar to the random real forcing,
replacing aleph_0 by lambda, so requiring it to be (<lambda)-complete. Of
course, we would welcome additional properties generalizing the ones of the
random real forcing. Returning to the ideal (instead forcing) we may look at
the Boolean Algebra of lambda-Borel sets modulo the ideal. Surprisingly we get
an positive = existence answer for lambda a "mild" large cardinals: the weakly
compact ones. We apply this to get consistency results on cardinal invariants
for such lambda's. We shall deal with other cardinals more properties related
forcing notions in a continuation.
