Some remarks on countably determined measures and uniform distribution of sequences

Two topics are investigated: countably determined (regular Borel probability) measures on compact Hausdorff spaces, and uniform distribution of sequences regarding mainly this kind of measures. We prove several characterizations of countably determined measures, and apply the results in order to show the existence of a well distributed sequence in the support of a countably determined measure. We also generalize a result of Losert on the existence of uniformly distributed sequences in compact dyadic spaces.     

On the measure theoretic structure of compact groups

If is a compact group with , we show the following results:

(i)

There exist direct products of compact metric groups and continuous open surjections with respect to Haar measure; and

(ii)

the Haar measure on is Baire and at the same time Jordan isomorphic to the Haar measure on a direct product of compact Lie groups.

Applications of the above results in measure theory are given.

     

Developing a step-by-step effectiveness assessment model for customer-oriented service organizations

Effectiveness involves more than simple efficiency, which is limited to the production process assessment of peer operational units. Effectiveness incorporates variables that are both controllable (i.e. efficiency) and non-controllable (i.e. perceived quality) by the operational units. It is a fundamental driver for the success of either a for-profit or a non-for-profit unit in a competitive environment that is customer/citizen- and goal-oriented. Additionally, with respect to the short-run production constraints, i.e. the resources available and controllable by the operational units, and the legal status, we go beyond the traditional effectiveness assessment techniques by developing a Modified or “rational” Quality-driven-Efficiency-adjusted Data Envelopment Analysis (MQE-DEA) model. This particular model provides in the short run a feasible effectiveness attainment path for every disqualified unit in order to meet high-perceived quality and high-efficiency standards. By applying the MQE-DEA model a new production equilibrium is determined, which is different from the equilibrium suggested by the mainstream microeconomic theory, in that it takes into account not only the need for operational efficiency but also the customer-driven market dynamics.     

Bank-level estimates of market power

The aim of this study is to provide an empirical methodology for the estimation of market power of individual banks. The new method employs the well-known model of Panzar and Rosse (1987) and proposes its estimation using the local regression technique. Local regression yields coefficient estimates equal to the number of observations and, thus, market power is estimated for each bank at each point in time. In addition, a number of restrictive assumptions regarding the properties of the production function of banks are relaxed. A panel of banks from transition countries that has been recently employed by Delis (2010) to obtain market power estimates using the Panzar and Rosse model at the country level is used for comparative purposes. We find that country averages of the bank-level results exhibit a very close relationship with standard, industry-level Panzar-Rosse estimates. However, the empirical results suggest that many banks in countries with fairly competitive banking systems deviate significantly from the country averages and that market power varies substantially across banks in each country.     

Reznichenko families of trees and their applications

Examples of Talagrand, Gul'ko and Corson compacta resulting from Reznichenko families of trees are presented. The K_σδ property for weakly -analytic Banach spaces with an unconditional basis is proved.     

Technical and allocative efficiency in European banking

This paper specifies an empirical framework for estimating both technical and allocative efficiency using the translog cost-share system, thus providing a solution to the issue known in the literature as the Greene problem. The model is applied to a large panel of European banks and the results are compared with those of a model that does not include an allocative inefficiency term and also with those obtained by using a consistent Bayesian technique. Our results suggest that models which include only technical efficiency, significantly overestimate it, while parameter estimates from the model that includes both technical and allocative efficiency are very close to the ones obtained from the Bayesian approach, thus enhancing our confidence in the proposed methodology. Finally, the fact that allocative efficiency of banks in our sample improves more than technical efficiency underlines the importance of including an allocative inefficiency component in parametric efficiency models.     

Convex unconditionality and summability of weakly null sequences

It is proved that every normalized weakly null sequence has a subsequence which is convexly unconditional. Further, a hierarchy of summability methods is introduced and with this we give a complete classification of the complexity of weakly null sequences.     

On some generalizations of Lorentz's almost convergence

We investigate an extension of the almost convergence of G.G. Lorentz, further weakening the notion of M-almost convergence we defined in [S. Mercourakis, G. Vassiliadis, An extension of Lorentz's almost convergence and applications in Banach spaces, Serdica Math. J. 32 (2006) 71–98] and requiring that the means of a bounded sequence restricted on a subset M of converge weakly in ℓ^∞(M). The case when M has density 1 is of special interest and in this case we derive a result in the direction of the Mean Ergodic Theorem (see Theorem 2).     

Examples concerning heredity problems of WCG Banach spaces

We present two examples of WCG spaces that are not hereditarily WCG. The first is a space with an unconditional basis, and the second is a space such that is WCG and does not contain . The non-WCG subspace of has the additional property that is not WCG and is reflexive.