Dual representation of monotone convex functions on 𝐿⁰

Kupper, Michael; Svindland, Gregor

doi:10.1090/S0002-9939-2011-10835-9

Dual representation of monotone convex functions on $L^0$
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by Michael Kupper and Gregor Svindland

Proc. Amer. Math. Soc. 139 (2011), 4073-4086

DOI: https://doi.org/10.1090/S0002-9939-2011-10835-9

Published electronically: April 12, 2011

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Abstract:

We study monotone convex functions $\psi :{L}^0(\Omega ,\mathcal {F} ,\mathbb {P})\to (-\infty ,\infty ]$ and derive a dual representation as well as conditions that ensure the existence of a $\sigma$-additive subgradient. The results are motivated by applications in economic agents’ choice theory.

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