منابع مشابه
Gromov-Hausdorff Convergence of Discrete Transportation Metrics
This paper continues the investigation of ‘Wasserstein-like’ transportation distances for probability measures on discrete sets. We prove that the discrete transportation metrics on the d-dimensional discrete torus TN with mesh size 1 N converge, when N → ∞, to the standard 2-Wasserstein distance on the continuous torus in the sense of Gromov– Hausdorff. This is the first result of a passage to...
متن کاملDiscrete Lyapunov exponents and Hausdorff dimension *
A major concept in differentiable dynamics is the Lyapunov exponents of a given map f . It combines the results of ergodic theory with differential properties of f . Consider the following two closely related examples which motivate our paper. Let M be a compact surface and f : M → M a smooth diffeomorphism. Let E denote the set of Borel f -invariant ergodic measures on M . Assume that μ ∈ E . ...
متن کاملNatural Transformations. Discrete Categories
We present well known concepts of category theory: natural transofmations and functor categories, and prove propositions related to. Because of the formalization it proved to be convenient to introduce some auxiliary notions, for instance: transformations. We mean by a transformation of a functor F to a functor G, both covariant functors from A to B, a function mapping the objects of A to the m...
متن کاملDiscrete Spectrum Transformations
An important problem in ergodic theory is to find classifications of various types of measure preserving transformations. An example of this is the theorem of Ornstein that two Bernoulli shifts are isomorphic iff they have the same entropy. So a Bernoulli shift can be assigned a real number that completely determines its isomorphism type. Can this be done for other types of transformations? Per...
متن کاملTransformations of Discrete Closure Systems
Discrete systems such as sets, monoids, groups are familiar categories. The internal structure of the latter two is defined by an algebraic operator. In this paper we concentrate on discrete systems that are characterized by unary operators; these include choice operators σ, encountered in economics and social theory, and closure operators φ, encountered in discrete geometry and data mining. Be...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1973
ISSN: 0002-9939
DOI: 10.2307/2038946