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RIESZ SPACES AND ELEMENTARY INTEGRALS 2
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absolutely continuous adequate algebra assume B-continuous Banach space belongs bounded called classes Clearly closed coincide compact compact sets complete conditional expectation consider consists contains continuous with respect converges Corollary countable cover defined Definition denote dense derivative directed disjoint dominated element equal equivalent essential everywhere evidently Example exists extension field finite variation fixed function f given Hence holds implies increasing integrable sets integration lattice Lemma lifting limit linear map locally majorized martingale norm points positive positive measure projective Proof properties Proposition proved result Riesz space RM)-adequate RM)-integrable satisfies separable sequence statement step functions strong subset Suppose supremum theorem theory tight tight measures topology uniform uniformly continuous union unique upper integral values weak upper gauge zero