1 Measure Theory 2 1.1 σ-Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Dynkin Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Probability Measures . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5 Measurable Maps and Induced Measures . . . . . . . . . . . . . ....

We provide examples of homogeneous spaces which are neither symmetric spaces nor real cohomology spheres, yet have the property that every invariant metric is geometrically formal. We also extend the known obstructions to geometric formality to some new classes of homogeneous spaces and of biquotients, and to certain sphere bundles.

Recent work in the field of middleware technology proposes semantic spaces as a tool for coping with the scalability, heterogeneity and dynamism issues of large scale distributed environments. Reflective middleware moreover offers answers to the needs for adaptivity and self-determination of systems. Based on experiences with traditional middleware we argue that ontology-driven management is a ...

The realization of software projects can be significantly eased by extending the focus of reuse to architectural aspects instead of concentrating on separate software elements. Yet in any case, operational techniques are required to support the retrieval and selection of reusable items. To this end, we extend on the concept of design spaces which allows to describe the relevant properties of so...

The examples of topological spaces that we construct in this exposition arose simultaneously from two seemingly disparate fields: the first author, in his thesis [1], discovered these spaces after working with H. Landau, Z. Landau, J. Pommersheim, and E. Zaslow on problems about random walks on graphs [2]. The second author discovered these same spaces while collaborating with D. Koditschek in ...

We define algebraic cobordism of classifying spaces, Ω∗(BG) and G-equivariant algebraic cobordism Ω∗G(−) for a linear algebraic group G. We prove some properties of the coniveau filtration on algebraic cobordism, denoted F (Ω(−)), which are required for the definition to work. We show that G-equivariant cobordism satisfies the localization exact sequence. We calculate Ω(BG) for algebraic groups...

People can derive a great deal of value from social interactions. This paper discusses how one might “seed” online environments to be rich in social interaction. The argument presented is based on an analysis of research on the support of collaboration among distributed work teams. This revealed four elements that may contribute towards for fostering interaction among team members: place-making...

A well known application of Ramsey’s Theorem to Banach Space Theory is the notion of a spreading model (ẽi) of a normalized basic sequence (xi) in a Banach space X. We show how to generalize the construction to define a new creature (ei), which we call an asymptotic model of X. Every spreading model of X is an asymptotic model of X and in most settings, such as if X is reflexive, every normaliz...

In the article concepts and facts necessary to continue formalization of theory of continuous lattices according to [11] are introduced. and [4] provide the notation and terminology for this paper. 1. PRELIMINARIES The following two propositions are true: (1) For all sets X, A, B such that A ∈ Fin X and B ⊆ A holds B ∈ Fin X. (2) For every set X and for every family F of subsets of X such that ...

ADDRESSING UTILITY SPACE COMPLEXITY IN NEGOTIATIONS INVOLVING HIGHLY UNCORRELATED, CONSTRAINT-BASED UTILITY SPACES IVAN MARSA-MAESTRE,1 MIGUEL A. LOPEZ-CARMONA,1 MARK KLEIN,2 TAKAYUKI ITO,3 AND KATSUHIDE FUJITA3 1Computer Engineering Department, Universidad de Alcala, Madrid, Spain 2Center for Collective Intelligence, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA 3School ...