Let X be a locally connected, b-compact metric space and E a closed subset of X. Let G be the space of all continuous real-valued functions defined on some closed subsets of E. We prove the equivalence of the τ aw and τ K topologies on G, where τ aw is the so called Attouch-Wets topology, defined in terms of uniform convergence of distance functionals, and τ K is the topology of Kuratowski conv...

Let X = {Xt, t≥ 0} be a càdlàg Lévy process, centered, with moments of all orders. There are two families of orthogonal polynomials associated with X. On one hand, the Kailath–Segall formula gives the relationship between the iterated integrals and the variations of order n ofX, and defines a family of polynomials P1(x1), P2(x1, x2), . . . that are orthogonal with respect to the joint law of th...

We show that if X is a Σ 1 separable metrizable space which is not σ-compact then C p (X), the space of bounded real-valued continuous functions on X with the topology of pointwise convergence, is Borel-Π 1 -complete. Assuming projective determinacy we show that if X is projective not σ-compact and n is least such that X is Σ1n then Cp(X), the space of real-valued continuous functions on X with...

We remark that the result presented here can be proved more simply using the closed graph theorem. However we believe that our results can be used to prove a more interesting result. Details to follow in a later paper. One of the remarkable features of the space of holomorphic functions (in either one or several variables) is that the standard Frechet space topologies— say, for example, the L o...

The paper sets up a two-region endogenous growth model to discuss growth and regional convergence of uni ed Germany. It emphasises the role of private and public capital accumulation during the developing process. The theoretical part derives scal policy rules which establish convergence of regional output per capital and convergence of regional human wealth. To assess the speed of convergence ...

This study examines the role of tourism development in reducing regional income inequality in China. First, the theoretical foundation for how tourism affects regional income inequality is discussed. Second, based on the conditional convergence framework, this study proposes a spatiotemporal autoregressive model to capture spatial and temporal dependence as well as spatial heterogeneity. Touris...

In this study, we analyze the development experience of eco-tourism in different regions of china to find the common regional convergence which is checked with ADF test and co-integration relations. In our results, we could contribute as theoretical foundation for regional development of ecotourism in China. Meanwhile, the research result of convergence of regional eco-agricultural tourism in C...

This study suggests a two-step approach to identifying and interpreting regional convergence clubs in Europe. The first step calculates Bayesian probabilities for various assignments of regions to two clubs using a general stochastic space-time dynamic panel relationship between growth rates and initial levels of income as well as endowments of physical, knowledge and human capital. This approa...

Employing the new regression tests for Convergence, Club Convergence and Clustering proposed by Phillips and Sul (2007), this paper models and analyzes the behavior of China‘s energy sectors. Energy market ̳convergence clusters‘ are identified using new price data and their regional spatial distributions are mapped for four major fuel types; coal, gasoline, diesel and electricity. It is found t...