Cauchy and Poisson integrals over {\it unbounded\/} sets are employed to prove Mittag-Leffler type theorems with massive singularities as well as approximation theorems for holomorphic and harmonic functions.

Keywords:

holomorphic, harmonic, Mittag-Leffler, Runge holomorphic, harmonic, Mittag-Leffler, Runge

MSC Classifications:

30F99, 31C12 show english descriptions None of the above, but in this section
Potential theory on Riemannian manifolds [See also 53C20; for Hodge theory, see 58A14] 30F99 - None of the above, but in this section
31C12 - Potential theory on Riemannian manifolds [See also 53C20; for Hodge theory, see 58A14]

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