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Functions inR2(E) and points of the fine interior

1988
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Pacific Journal of Mathematics
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Let E c C be a set that is compact in the usual topology. Let m denote 2-dimensional Lebesgue measure. We denote by Ro(E) the algebra of rational functions with poles off E. For p > 1, let L P {E) = L P (E, dm). The closure of R 0 {E) in L P {E) will be denoted by R p {E). In this paper we study the behavior of functions in R 2 (E) at points of the fine interior of E. We prove that if U C E is a finely open set of bounded point evaluations for R 2 (E) 9 then there is a finely open set V c U

doi:10.2140/pjm.1988.134.393
fatcat:toyoesr4hfdyjjf63gqdoyhlq4