Convergence to convex compact sets in infinite dimensions

Zvi Artstein; Vladimir Gaitsgory

doi:10.1016/S0022-247X(03)00334-2

Convergence to convex compact sets in infinite dimensions

Zvi Artstein^*, Vladimir Gaitsgory

^*Corresponding author for this work

Research output: Contribution to journal › Article

5 Citations (Scopus)

Abstract

We provide a simple test for the convergence of a sequence of subsets in an infinite-dimensional space to a compact convex one. The test reduces, roughly, the convergence problem to finite dimensions. Applications are portrayed demonstrating how convexification phenomena established in finite dimensions are easily generalized to infinite dimensions.

Original language	English
Pages (from-to)	471-480
Number of pages	10
Journal	Journal of Mathematical Analysis and Applications
Volume	284
Issue number	2
DOIs	https://doi.org/10.1016/S0022-247X(03)00334-2
Publication status	Published - 15 Aug 2003
Externally published	Yes

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10.1016/S0022-247X(03)00334-2

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title = "Convergence to convex compact sets in infinite dimensions",

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AU - Gaitsgory, Vladimir

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AB - We provide a simple test for the convergence of a sequence of subsets in an infinite-dimensional space to a compact convex one. The test reduces, roughly, the convergence problem to finite dimensions. Applications are portrayed demonstrating how convexification phenomena established in finite dimensions are easily generalized to infinite dimensions.

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DO - 10.1016/S0022-247X(03)00334-2

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EP - 480

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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