Limit spaces with approximations

Limit spaces with approximations

Polish spaces, computable approximations, and bitopological spaces

Answering a question of J. Lawson (formulated also earlier, in 1984, by Kamimura and Tang [Theoret. Comput. Sci. 34 (1984) 275–288]) we show that every Polish space admits a bounded complete computational model, as defined below. This results from our construction, in each Polish space 〈X,τ 〉, of a countable family C of non-empty closed subsets of X such that: (cp) each subset of C with the fin...

Central Limit Theorem and Diophantine Approximations

Let Fn denote the distribution function of the normalized sum Zn = (X1+ · · ·+Xn)/σ √ n of i.i.d. random variables with finite fourth absolute moment. In this paper, polynomial rates of convergence of Fn to the normal law with respect to the Kolmogorov distance, as well as polynomial approximations of Fn by the Edgeworth corrections (modulo logarithmically growing factors in n) are given in ter...

Limit spaces and transfinite types

We give a characterisation of an extension of the Kleene-Kreisel continuous functionals to objects of transfinite types using limit spaces of transfinite types.

Blackwell Spaces and -Approximations of Markov Chains