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<p>Edwards’s Theorem establishes a duality between a positive cone of upper semi-continuous functions on compact spaces and its Jensen measures. This paper investigates an extension of Edwards’s Theorem to the setting of Banach lattice-valued functions. To facilitate this extension, we introduce two notions of upper semi-continuity tailored for functions mapping into Dedekind complete Riesz spaces. Furthermore, we demonstrate that this framework yields a characterization of the supremum of certain families of functions in terms of their operator-valued Jensen measures and lower envelopes.</p>

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Edwards’s Theorem in Banach Lattice Setting

  • 期刊论文

  • 发表日期：

    2026年7月1日

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  • Umutcan Erdur,
  • Nihat Gökhan Göğüş

摘要

Edwards’s Theorem establishes a duality between a positive cone of upper semi-continuous functions on compact spaces and its Jensen measures. This paper investigates an extension of Edwards’s Theorem to the setting of Banach lattice-valued functions. To facilitate this extension, we introduce two notions of upper semi-continuity tailored for functions mapping into Dedekind complete Riesz spaces. Furthermore, we demonstrate that this framework yields a characterization of the supremum of certain families of functions in terms of their operator-valued Jensen measures and lower envelopes.