A result of J. Bourgain: has the Dunford-Pettis property
Weak compactness implies strong compactness in the space of uniform measures
On some classical measure-theoretic theorems for non-sigma-complete Boolean algebras
CONTENTSIntroduction...................................................................................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....
Supporteurs des prodistributions et mesures cylindriques
A characterisation of the closure of in
Addendum to the paper : “On certain probabilities equivalent to Wiener measure”
On certain probabilities equivalent to Wiener measure, d'après Dubins, Feldman, Smorodinsky and Tsirelson
For a Banach space isomorphic to its square the Radon-Nikodým property and the Krein-Milman property are equivalent
The class of Banach spaces, which do not have c0 as a spreading model, is not L2-hereditary
A remark on Tsirelson's stochastic differential equation
Brownian filtrations are not stable under equivalent time-changes
A bipolar theorem for L
An inequality for the predictable projection of an adapted process
A general version of the fundamental theorem of asset pricing.
On Vershik's standardness criterion and Tsirelson's notion of cosiness
The Banach space of workable contingent claims in arbitrage theory
A generalized dual maximizer for the Monge–Kantorovich transport problem
The dual attainment of the Monge–Kantorovich transport problem is analyzed in a general setting. The spaces are assumed to be polish and equipped with Borel probability measures and . The transport cost function : × → [0,∞] is assumed to be Borel measurable. We show that a dual optimizer always exists, provided we interpret it as a projective limit of certain finitely additive measures. Our methods are functional analytic and rely on Fenchel’s perturbation technique.
Functions in and associated convolution operators
A general duality theorem for the Monge-Kantorovich transport problem
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...
Hiding a constant drift
The following question is due to Marc Yor: Let be a brownian motion and =+ . Can we define an -predictable process such that the resulting stochastic integral (⋅) is a brownian motion (without drift) in its own filtration, i.e. an -brownian motion? In this paper we show that by dropping the requirement of -predictability of we can give a positive answer to this question. In other words, we are able to show that there is a weak solution to Yor’s question. The original...
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