In mathematics, especially the theory of several complex variables, the Oka–Weil theorem is a result about the uniform convergence of holomorphic functions on Stein spaces due to Kiyoshi Oka and André Weil.
The Oka–Weil theorem states that if X is a Stein space and K is a compact
-convex subset of X, then every holomorphic function in an open neighborhood of K can be approximated uniformly on K by holomorphic functions on
[1] Since Runge's theorem may not hold for several complex variables, the Oka–Weil theorem is often used as an approximation theorem for several complex variables.
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