Abstract
The paper shows that for any Gδ set F of Lebesgue measure zero on the unit circle T there exists a function f ∈ H∞ such that the radial limits of f exist at each point of T and vanish precisely on F . This solves a problem proposed by Rubel in 1973.
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More From: Annales Academiae Scientiarum Fennicae Mathematica
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