A note on strong extreme and strongly exposed points in Bochner 𝐿^{𝑝}-spaces

Abstract

A strongly exposed (strongly extreme) vector-valued <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Superscript p"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{L^p}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -function takes only strongly exposed (strongly extreme) values almost everywhere on its support. We remove the restrictions, concerning the range space and the measure, in previous papers of the author and M. A. Smith.