Abstract
Using complex methods combined with Baire’s Theorem, we show that one-sided extendability, extendability, and real analyticity are rare phenomena on various spaces of functions in the topological sense. These considerations led us to introduce the p-continuous analytic capacity and variants of it, pin {0,1,2, ldots }cup {infty }, for compact or closed sets in mathbb {C}. We use these capacities in order to characterize the removability of singularities of functions in the spaces A^p .
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