On standard measure spaces every order continuous linear map between two ideals of almost everywhere finite measurable functions can be represented by a random measure. An analogue of this theorem is proved for the case of arbitrary σ-finite measure spaces. This fact leads to a proof that every order continuous linear map between ideals of almost everywhere finite measurable functions on σ-finite measure spaces is multiplication conditional expectation representable. This sheds further light on the structure of order continuous operators.
Positivity – Springer Journals
Published: Mar 23, 2005
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