The existence of an inverse limit of inverse system of measure spaces - a purely measurable case

The existence of an inverse limit of an inverse system of (probability) measure spaces has been investigated since the very beginning of the birth of the modern probability theory. Results from Kolmogorov [10], Bochner [2], Choksi [5], Metivier [14], Bourbaki [3] among others have paved the way of the deep understanding of the problem under consideration. All the above results, however, call for some topological concepts, or at least ones which are closely related topological ones. In this paper we investigate purely measurable inverse systems of (probability) measure spaces, and give a sucient condition for the existence of a unique inverse limit. An example for the considered purely measurable inverse systems of (probability) measure spaces is also given.

Az ajánlati könyv statisztikai tulajdonságai (Statistical properties of the limit order book)

A pénzügyi modellek jelentős része feltételezi a piacok hatékony működését. Ennek következtében számos tudományos kutatás központi témája volt a piacok hatékonyságának tesztelése és ennek igazolása, esetleg cáfolata. Ezen próbálkozások azonban mind a mai napig eredménytelenül zárultak. A tesztelések nyomán a kutatások a termékek áralakulásából indultak ki, és a hozamokat ezen keresztül elemezték. Az elmúlt években azonban a fókusz átterelődött az árak alakulásáról egy elemibb tényezőre, az ajánlati könyvre. Ugyanis végső soron az ajánlatvezérelt piacokon az árakat az ajánlati könyvbe benyújtott megbízások alakulása fogja meghatározni. Mivel a tőzsdék jelentős része ajánlatvezérelt piacként működik, ezért érdemesnek tartották a kutatók, hogy inkább az ajánlati könyv alakulásának statisztikai jellemzőit elemezzék, hátha az eredményre vezet, és sikerül közelebb jutni a hatékony piacok elméletének igazolásához vagy cáfolatához. Jelen tanulmány célja az, hogy az eddig megjelent tudományos kutatások alapján ismertesse az ajánlati könyv alapvető statisztikai tulajdonságait, és rávilágítson arra: mindez valójában hozzájárult-e a hatékony piacok elméletének igazolásához? ______ Most of the fi nancial models assume that markets are effi cient. As a result, numerous scientifi c researchers were focused on testing the effi cient market hypothesis, and tried to prove, or deny it. However, all these attempts are still unsuccessful. During these researches, the analyses of the effi cient market hypothesis were based on the price evolution of a certain asset, and through this the returns were examined. In the recent years the research interest has changed, and instead of analyzing the returns, a more primary factor got into focus, namely the limit order book. The reason is that on order driven markets the prices and the order sizes in the limit order book infl uence the price evolution on the market. Since a notable number of stock markets operate as an order driven market, the researchers thought that it worth analyzing the statistical properties of the limit order book, because maybe it will get us closer to the proof of the effi cient market hypothesis. The purpose of this study is to summarize the statistical properties of the limit order book, based on the scientifi c works published so far. The study would like to highlight whether these studies contributed to the proof or disproof of the effi cient market hypothesis.

Borrowing services from nature. Methodologies to evaluate ecosystem services focusing on Hungarian case studies.

In modern societies, humans are largely managing the world's natu­ral resources as if they were limitless. ln fact, even the so-called renewable resources require time tor renewal once they have been used. This kind of human attitude puts pressure on Earth's ecosystems at an unprecedented scale. In order to reverse the recent trend, policies shall tackle the roots of the problems and the drivers behind them must be addressed in order to reduce the pressure on ecosystems, including the overuse of natural resources and ecological space. This publication aims to show good examples tor evaluating natural values and tor showing possible environmental and social impacts of various policies. Considering carefully the examples presented in this publication could play fundamental role in proper decision making that considers environmental and overall sustainability aspects.