Edwards's theorem in Banach lattice setting

Official URL: https://dx.doi.org/10.1007/s00009-026-03152-w

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.