In the sequel we prove that if a Blaschke product B is continuous in the closed unit disk except on a closed set E is contained in T of measure zero, then B is contained in 9K, where K denotes the closed convex hull of the interpolating Blaschke products. Moreover, we show that a generic Blaschke product is contained in 21K. By the well-known theorem of Marshall, this implies that the unit ball of H~∞ is contained in 27K. The proofs employ a technical result, given in Section 3, which may be of some independent interest. The results in the paper improve earlier work in [8], [4], and [10]. We refer to these papers and to [3] for further background on the questions treated here.
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