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Displaying 1 – 20 of 38

A categorical approach to integration.

Börger, Reinhard (2010)

Theory and Applications of Categories [electronic only]

A Choquet Ordering and Unique Decompositions in Convex sets of Tight Measures

Gerhard Winkler (1980)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

A probabilistic ergodic decomposition result

Albert Raugi (2009)

Annales de l'I.H.P. Probabilités et statistiques

Let $(X, 𝔛, μ)$ be a standard probability space. We say that a sub-σ-algebra $𝔅$ of $𝔛$ decomposes μ in an ergodic way if any regular conditional probability $^{𝔅} P$ with respect to $𝔅$ andμ satisfies, for μ-almost every x∈X, $\forall B \in 𝔅,^{𝔅} P (x, B) \in {0, 1}$ . In this case the equality $μ (\cdot) = \int_{X}^{𝔅} P (x, \cdot) μ (d x)$ , gives us an integral decomposition in “ $𝔅$ -ergodic” components. For any sub-σ-algebra $𝔅$ of $𝔛$ , we denote by $\bar{𝔅}$ the smallest sub-σ-algebra of $𝔛$ containing $𝔅$ and the collection of all setsAin $𝔛$ satisfyingμ(A)=0. We say that $𝔅$ isμ-complete if $𝔅 = \bar{𝔅}$ . Let ${𝔅_{i} i \in I}$ be a non-empty family...

A uniqueness result for the continuity equation in two dimensions

Giovanni Alberti, Stefano Bianchini, Gianluca Crippa (2014)

Journal of the European Mathematical Society

We characterize the autonomous, divergence-free vector fields $b$ on the plane such that the Cauchy problem for the continuity equation $\partial_{t} u + \frac{.}{\dot{}} (b u) = 0$ admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential $f$ associated to $b$ . As a corollary we obtain uniqueness under the assumption that the curl of $b$ is a measure. This result can be extended to certain non-autonomous vector fields $b$ with bounded divergence....

An exact functional Radon-Nikodym theorem for Daniell integrals

E. de Amo, I. Chitescu, M. Díaz Carrillo (2001)

Studia Mathematica

Given two positive Daniell integrals I and J, with J absolutely continuous with respect to I, we find sufficient conditions in order to obtain an exact Radon-Nikodym derivative f of J with respect to I. The procedure of obtaining f is constructive.

Application de l'existence d'un relèvement à un théorème sur la désintégration des mesures

Jean Pellaumail (1972)

Annales de l'I.H.P. Probabilités et statistiques

Characterization of optimal shapes and masses through Monge-Kantorovich equation

Guy Bouchitté, Giuseppe Buttazzo (2001)

Journal of the European Mathematical Society

We study some problems of optimal distribution of masses, and we show that they can be characterized by a suitable Monge-Kantorovich equation. In the case of scalar state functions, we show the equivalence with a mass transport problem, emphasizing its geometrical approach through geodesics. The case of elasticity, where the state function is vector valued, is also considered. In both cases some examples are presented.