Abstract
<abstract><p>We were interested in Bernstein and Lévy measures having certain convexity-type properties. The convexity-type properties were an extension of the harmonic convexity property considered in <sup>[<xref ref-type="bibr" rid="b9">9</xref>]</sup>. We characterized the corresponding completely monotone and Bernstein functions. We hope this paper can aid with understanding the analogous properties and open questions presented in <sup>[<xref ref-type="bibr" rid="b8">8</xref>,<xref ref-type="bibr" rid="b9">9</xref>]</sup>.</p></abstract>
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