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The Relationship between $ε$-Kronecker and Sidon Sets

A subset $E$ of a discrete abelian group is called $ε$-Kronecker if all $E$-functions of modulus one can be approximated to within $ε$ by characters. $E$ is called a Sidon set if all bounded $E$-functions can be interpolated by the Fourier transform of measures on the dual group. As $ε$-Kronecker sets with $ε<2$ possess the same arithmetic properties as Sidon sets, it is natural to ask if they are Sidon. We use the Pisier net characterization of Sidonicity to prove this is true.