A Fubini-type theorem for finitely additive measure spaces
A Generalization Of Fubini's Theorem For Banach Algebra-Valued Measures.
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 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 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.
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 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 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...
A Measure Space Without the Strong Lifting Property.
A note on Carathéodory type function
A note on Talagrand's concentration inequality.
A note on the Ehrhard inequality
We prove that for λ ∈ [0,1] and A, B two Borel sets in with A convex, , where is the canonical gaussian measure in and is the inverse of the gaussian distribution function.
A property of doubly stochastic densities
A refinement of Jensen's inequality.
A saddle-point approach to the Monge-Kantorovich optimal transport problem
The Monge-Kantorovich problem is revisited by means of a variant of the saddle-point method without appealing to c-conjugates. A new abstract characterization of the optimal plans is obtained in the case where the cost function takes infinite values. It leads us to new explicit sufficient and necessary optimality conditions. As by-products, we obtain a new proof of the well-known Kantorovich dual equality and an improvement of the convergence of the minimizing sequences.
A saddle-point approach to the Monge-Kantorovich optimal transport problem
The Monge-Kantorovich problem is revisited by means of a variant of the saddle-point method without appealing to c-conjugates. A new abstract characterization of the optimal plans is obtained in the case where the cost function takes infinite values. It leads us to new explicit sufficient and necessary optimality conditions. As by-products, we obtain a new proof of the well-known Kantorovich dual equality and an improvement of the convergence of the minimizing sequences.
A simplified multidimensional integral
We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained more quickly. We also give a characterization of the integrable functions and their primitives.
Almost Everywhere Convergence of Riesz-Raikov Series
Let T be a d×d matrix with integer entries and with eigenvalues >1 in modulus. Let f be a lipschitzian function of positive order. We prove that the series converges almost everywhere with respect to Lebesgue measure provided that .
An elementary proof of the Fubini-Stone theorem
An extension of the Steinhaus-Weil theorem
Analyse des correspondances et codage par une probabilité de transition
Approximate isometries on bounded sets with an application to measure theory