  We discuss quantum theory of fields \phi defined on (d+1)-dimensional
manifold {\cal M} with a boundary {\cal B}. The free action W_{0}(\phi) which
is a bilinear form in \phi defines the Gaussian measure with a covariance
(Green function) {\cal G}. We discuss a relation between the quantum field
theory with a fixed boundary condition \Phi and the theory defined by the Green
function {\cal G}. It is shown that the latter results by an average over \Phi
of the first. The QFT in (anti)de Sitter space is treated as an example. It is
shown that quantum fields on the boundary are more regular than the ones on
(anti) de Sitter space.
