Iterated Fine Limits and Iterated Nontangential Limits

On Iterated Limits of Subsets of a Convergence -group

In this paper we deal with the relation lim α lim α X = lim α X for a subset X of G, where G is an -group and α is a sequential convergence on G.

Analytic Contractions, Nontangential Limits, and the Index of Invariant Subspaces

Let H be a Hilbert space of analytic functions on the open unit disc D such that the operator Mζ of multiplication with the identity function ζ defines a contraction operator. In terms of the reproducing kernel for H we will characterize the largest set ∆(H) ⊆ ∂D such that for each f, g ∈ H, g 6= 0 the meromorphic function f/g has nontangential limits a.e. on ∆(H). We will see that the question...

Generalized Covering Groups and Direct Limits

Ratio limits and simulation algorithms for the Palm version of stationary iterated tessellations

Distributional properties and a simulation algorithm for the Palm version of stationary iterated tessellations are considered. In particular we study the limit behavior of functionals related to Cox-Voronoi cells (such as typical shortest path lengths) if either the intensity γ0 of the initial tessellation or the intensity γ1 of the component tessellation converges to 0. We develop an explicit ...

Iterated Local Reeection Vs Iterated Consistency

For \natural enough" systems of ordinal notation we show that times iterated local reeection schema over a suuciently strong arithmetic T proves the same 0 1-sentences as ! times iterated consistency. A corollary is that the two hierarchies catch up modulo relative interpretability exactly at-numbers. We also derive the following more general \mixed" formulas estimating the consistency strength...