The Dirichlet product of functions on a semi-Riemann domain and generalized Euler vector fields, which include the radial, [`(¶)]\bar{\partial} -Euler, and the [`(¶)]\bar{\partial} -Neumann vector fields, are introduced. The integral means and the harmonic residues of functions on a Riemann domain are studied. The notion of semi-harmonicity of functions on a complex space is introduced. It is shown that, on a Riemann domain, the semi-harmonicity of a locally integrable function is characterized by local mean-value properties as well as by weak harmonicity. In particular, the Weyl’s Lemma is extended to a Riemann domain.