In this paper we introduce three classes of Banach analytic spaces: hyperbolic Banach analytic spaces, weakly taut spaces and Banach analytic spaces having Vitali's property. At the same time, we establish some relations between these three classes. Finally, we give some conditions under which balanced Hartogs domains in Banach spaces are weakly taut.
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Hai et al. (2016) studied this question.
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