Feynman diagrams and large order estimates for the exponential anharmonic oscillator
Feynman maps, Cameron-Martin formulae and anharmonic oscillators
Fibrés dynamiques. Entropie et dimension
Fields of sets, set functions, set function integrals, and finite additivity.
Fields with analytic structure
Filippov Lemma for certain second order differential inclusions
In the paper we give an analogue of the Filippov Lemma for the second order differential inclusions with the initial conditions y(0) = 0, y′(0) = 0, where the matrix A ∈ ℝd×d and multifunction is Lipschitz continuous in y with a t-independent constant l. The main result is the following: Assume that F is measurable in t and integrably bounded. Let y 0 ∈ W 2,1 be an arbitrary function fulfilling the above initial conditions and such that where p 0 ∈ L 1[0, 1]. Then there exists a solution y ∈ W 2,1...
Filters and sequences
We consider two situations which relate properties of filters with properties of the limit operators with respect to these filters. In the first one, we show that the space of sequences having limits with respect to a filter is itself and therefore, by a result of Dobrowolski and Marciszewski, such spaces are topologically indistinguishable. This answers a question of Dobrowolski and Marciszewski. In the second one, we characterize universally measurable filters which fulfill Fatou’s lemma.
Finitarily Bernoulli factors are dense
It is not known if every finitary factor of a Bernoulli scheme is finitarily isomorphic to a Bernoulli scheme (is finitarily Bernoulli). In this paper, for any Bernoulli scheme X, we define a metric on the finitary factor maps from X. We show that for any finitary map f: X → Y, there exists a sequence of finitary maps fₙ: X → Y(n) that converges to f, where each Y(n) is finitarily Bernoulli. Thus, the maps to finitarily Bernoulli factors are dense. Let (X(n)) be a sequence of Bernoulli schemes such...
Finitary orbit equivalence and measured Bratteli diagrams
We prove a strengthened version of Dye's theorem on orbit equivalence, showing that if the transformation structures are represented as finite coordinate change equivalence relations of ergodic measured Bratteli diagrams, then there is a finitary orbit equivalence between these diagrams.
Finite Gauss measure on the space of interval exchange transformations. Lyapunov exponents
We construct a map on the space of interval exchange transformations, which generalizes the classical map on the interval, related to continued fraction expansion. This map is based on Rauzy induction, but unlike its relative kown up to now, the map is ergodic with respect to some finite absolutely continuous measure on the space of interval exchange transformations. We present the prescription for calculation of this measure based on technique developed by W. Veech for Rauzy induction.We study...
Finite generators of ergodic endomorphisms
Finite Procedures for Sofic Systems.
Finite Product of Semiring of Sets
We formalize that the image of a semiring of sets [17] by an injective function is a semiring of sets.We offer a non-trivial example of a semiring of sets in a topological space [21]. Finally, we show that the finite product of a semiring of sets is also a semiring of sets [21] and that the finite product of a classical semiring of sets [8] is a classical semiring of sets. In this case, we use here the notation from the book of Aliprantis and Border [1].
Finite rank actions and the loosely Bernoulli property.
Finite rank transformation and weak closure theorem
Finite return times for measure-preserving transformations.
Finitely additive invariant measures. I
Finitely additive invariant measures. II
Finitely subadditive outer measures, finitely superadditive inner measures and their measurable sets.
Finitely-additive, countably-additive and internal probability measures
We discuss two ways to construct standard probability measures, called push-down measures, from internal probability measures. We show that the Wasserstein distance between an internal probability measure and its push-down measure is infinitesimal. As an application to standard probability theory, we show that every finitely-additive Borel probability measure on a separable metric space is a limit of a sequence of countably-additive Borel probability measures in the sense that for all bounded...