  The derivation of the Helmholtz theorem of vector decomposition of a 3-vector
field requires that the field satisfy certain convergence properties at spatial
infinity. This paper investigates if time-dependent electromagnetic radiation
wave fields, which are of long range, satisfy these requirements. It is found
that the requirements are satisfied because the fields give rise to integrals
over the radial distance r of integrands of the form sin(kr)/r and cos(kr)/r.
These Dirichlet integrals converge at infinity as required.
