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On some classical measure-theoretic theorems for non-sigma-complete Boolean algebras

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Schachermayer W.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS Introduction...................................................................................5 §1. Preliminaries...........................................................................7 §2. Definitions and a theorem of Diestel, Faires and Huff.............9 §3. Examples...............................................................................13 §4. Some special classes of Boolean algebras ..........................19 §5. The Grothendieck property...................................................22 §6. The Orlicz-Pettis property ....................................................27 References.................................................................................32

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For a Banach space isomorphic to its square the Radon-Nikodým property and the Krein-Milman property are equivalent

60%

Schachermayer W.

Studia Mathematica

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1985

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tom 81

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nr 3

329-339

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A general duality theorem for the Monge-Kantorovich transport problem

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Beiglböck M., Léonard C., Schachermayer W.

Studia Mathematica

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2012

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tom 209

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nr 2

151-167

EN

The duality theory for the Monge-Kantorovich transport problem is analyzed in a general setting. The spaces X,Y are assumed to be Polish and equipped with Borel probability measures μ and ν. The transport cost function c: X × Y → [0,∞] is assumed to be Borel. Our main result states that in this setting there is no duality gap provided the optimal transport problem is formulated in a suitably relaxed way. The relaxed transport problem is defined as the limiting cost of the partial transport of masses 1 - ε from (X,μ) to (Y,ν) as ε > 0 tends to zero. The classical duality theorems of H. Kellerer, where c is lower semicontinuous or uniformly bounded, quickly follow from these general results.

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Functions in $L^{∞}(G)$ and associated convolution operators

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Lust-Piquard F., Schachermayer W.

Studia Mathematica

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1989

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tom 93

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nr 2

109-136

Ograniczanie wyników

3 Studia Mathematica

4 Schachermayer W.

1 Beiglböck M.

1 Lust-Piquard F.

1 Léonard C.

1 2012

1 1989

1 1985

1 1982

On some classical measure-theoretic theorems for non-sigma-complete Boolean algebras

For a Banach space isomorphic to its square the Radon-Nikodým property and the Krein-Milman property are equivalent

A general duality theorem for the Monge-Kantorovich transport problem

Functions in $L^{∞}(G)$ and associated convolution operators