Let Ω be a domain in ℂ2. We prove the following theorem. If the envelope of holomorphy of Ω is schlicht over Ω, then the envelope is in fact schlicht. We provide examples showing that the conclusion of the theorem does not hold in ℂn, n > 2. Additionally, we show that the theorem cannot be generalized to provide information about domains in ℂ2 whose envelopes are multiply sheeted.
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