  This note establishes smooth approximation from above for J-plurisubharmonic
functions on an almost complex manifold (X,J). The following theorem is proved.
Suppose X is J-pseudoconvex, i.e., X admits a smooth strictly
J-plurisubharmonic exhaustion function. Let u be an (upper semi-continuous)
J-plurisubharmonic function on X. Then there exists a sequence {u_j} of smooth,
strictly J-plurisubharmonic functions point-wise decreasing down to u.
  On any almost complex manifold (X,J) each point has a fundamental
neighborhood system of J-pseudoconvex domains, and so the theorem above
establishes local smooth approximation on X.
  This result was proved in complex dimension 2 by the third author, who also
showed that the result would hold in general dimensions if a parallel result
for continuous approximation were known. This paper establishes the required
step by solving the obstacle problem.
