2020
DOI: 10.1080/02331934.2020.1727901
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L0-convex compactness and its applications to random convex optimization and random variational inequalities

Abstract: First, this paper introduces the notion of L 0 -convex compactness for a special class of closed convex subsets-closed L 0 -convex subsets of a Hausdorff topological module over the topological algebra L 0 (F, K), where L 0 (F, K) is the algebra of equivalence classes of random variables from a probability space (Ω, F, P ) to the scalar field K of real numbers or complex numbers, endowed with the topology of convergence in probability. Then, this paper continues to develop the theory of L 0convex compactness b… Show more

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Cited by 10 publications
(15 citation statements)
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References 31 publications
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“…Remark 5. 13 If the convex subset B is closed, then it is bounded in probability (which means that K 1 satisfies NUPBR) if and only if it is convexly compact; see [45] for further details. Now, we consider K 0 and (K α ) α>0 together.…”
Section: The Fundamental Theorem Of Asset Pricing On Banach Function Spacesmentioning
confidence: 99%
See 4 more Smart Citations
“…Remark 5. 13 If the convex subset B is closed, then it is bounded in probability (which means that K 1 satisfies NUPBR) if and only if it is convexly compact; see [45] for further details. Now, we consider K 0 and (K α ) α>0 together.…”
Section: The Fundamental Theorem Of Asset Pricing On Banach Function Spacesmentioning
confidence: 99%
“…Remark 6. 13 Let us have a closer look at the situation U = L ∞ . Suppose that the convex cone K 0 satisfies NFLVR.…”
Section: The Fundamental Theorem Of Asset Pricing On Banach Function Spacesmentioning
confidence: 99%
See 3 more Smart Citations