The paper establishes a linear lower bound on the number of atoms in extremal singular inner functions for the Krzyż conjecture and new equivalent conditions for its validity.
‘A Simple Proof of Two Generalized Borel-Cantelli Lem- mas’
2 Pith papers cite this work. Polarity classification is still indexing.
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Necessary and sufficient conditions on the generating measure are derived for eventual connectedness and almost-completeness of edge exchangeable graphs, with a sufficient condition for asymptotic normality of the vertex count.
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Structural aspects of extremal functions in the Krzy\.z conjecture
The paper establishes a linear lower bound on the number of atoms in extremal singular inner functions for the Krzyż conjecture and new equivalent conditions for its validity.
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Edge Exchangeable Graphs: Connectedness, Gaussianity and Completeness
Necessary and sufficient conditions on the generating measure are derived for eventual connectedness and almost-completeness of edge exchangeable graphs, with a sufficient condition for asymptotic normality of the vertex count.