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In mathematics, especially several complex variables, the Behnke–Stein theorem states that a union of an increasing sequence (i.e., ) of domains of holomorphy is again a domain of holomorphy. It was proved by Heinrich Behnke and Karl Stein in 1938.

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  • Satz von Behnke und Stein (de)
  • Behnke–Stein theorem (en)
  • ベーンケ＝シュタインの定理 (ja)
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  • In der Mathematik ist der Satz von Behnke und Stein ein Lehrsatz der Funktionentheorie. Er besagt, dass jede zusammenhängende offene Riemannsche Fläche eine Steinsche Mannigfaltigkeit ist. Benannt ist er nach Heinrich Behnke und Karl Stein, die ihn 1939 bewiesen. (de)
  • 数学の、特に多変数複素函数の分野におけるベーンケ＝シュタインの定理（ベーンケ＝シュタインのていり、英: Behnke–Stein theorem）とは、正則領域の増加列 （すなわち を満たすもの）は再び正則領域であることを述べた定理である。 この定理は、増加擬凸領域の合併が再び擬凸である事実と関係し、その事実とレヴィ問題によって証明することが出来る。しかし歴史的に見ると、この定理は実際はレヴィ問題を解くために用いられていた。 (ja)
  • In mathematics, especially several complex variables, the Behnke–Stein theorem states that a union of an increasing sequence (i.e., ) of domains of holomorphy is again a domain of holomorphy. It was proved by Heinrich Behnke and Karl Stein in 1938. (en)
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  • Behnke-Stein theorem (en)
  • Stein manifold (en)
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  • behnkesteintheorem (en)
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  • In mathematics, especially several complex variables, the Behnke–Stein theorem states that a union of an increasing sequence (i.e., ) of domains of holomorphy is again a domain of holomorphy. It was proved by Heinrich Behnke and Karl Stein in 1938. This is related to the fact that an increasing union of pseudoconvex domains is pseudoconvex and so it can be proven using that fact and the solution of the Levi problem. Though historically this theorem was in fact used to solve the Levi problem, and the theorem itself was proved using the Oka–Weil theorem. This theorem again holds for Stein manifolds, but it is not known if it holds for Stein space. (en)
  • In der Mathematik ist der Satz von Behnke und Stein ein Lehrsatz der Funktionentheorie. Er besagt, dass jede zusammenhängende offene Riemannsche Fläche eine Steinsche Mannigfaltigkeit ist. Benannt ist er nach Heinrich Behnke und Karl Stein, die ihn 1939 bewiesen. (de)
  • 数学の、特に多変数複素函数の分野におけるベーンケ＝シュタインの定理（ベーンケ＝シュタインのていり、英: Behnke–Stein theorem）とは、正則領域の増加列 （すなわち を満たすもの）は再び正則領域であることを述べた定理である。 この定理は、増加擬凸領域の合併が再び擬凸である事実と関係し、その事実とレヴィ問題によって証明することが出来る。しかし歴史的に見ると、この定理は実際はレヴィ問題を解くために用いられていた。 (ja)
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  • E.M. (en)
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  • Chirka (en)
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