As appropriate generalizations of convex combinations with uncountably many terms, we introduce the so-called Choquet combinations, decomposable and as well their corresponding hull operators acting on power sets Lebesgue-Bochner spaces. We show that coincides in finite-dimensional setting, yet tends to be larger infinite dimensions. also provide a quantitative characterization hull, without an...

In this talk I will discuss some interesting subsets of ω1 – club-sets, Borel subsets, stationary and bi-stationary subsets of ω1 – and the theorem about them that has been most useful to me over the years, called Fodor’s Theorem. The question “How many types of stationary sets exist in ω1?” will be a recurring theme. (Spoiler alert: there are uncountably many really distinct stationary subsets...

Wedevelop a theory of stability inmany-to-manymatchingmarkets. We give conditions under which the setwise-stable set, a core-like concept, is nonempty and can be approached through an algorithm. The usual core may be empty. The setwise-stable set coincides with the pairwise-stable set and with the predictions of a non-cooperative bargainingmodel. The setwise-stable set possesses the conflict/co...

It is well known that superposition coding, namely separately encoding the independent sources, is optimal for symmetric multilevel diversity coding (SMDC) (Yeung-Zhang 1999). However, the characterization of the coding rate region therein involves uncountably many linear inequalities and the constant term (i.e., the lower bound) in each inequality is given in terms of the solution of a linear ...

The main purpose of this investigation is to show that a pendulum, whose pivot oscillates vertically in a periodic fashion, has uncountably many chaotic orbits. The attribute chaotic is given according to the criterion we now describe. First, we associate to any orbit a finite or infinite sequence as follows. We write 1 or −1 every time the pendulum crosses the position of unstable equilibrium ...

Consistently there exists an uncountably chromatic graph of cardinality א1 which does not contain an uncountable infinitely connected subgraph.

The Friedmann equation for a positive tension brane world with and without the Z2 symmetry is derived and the possible effects of dropping the Z2 symmetry on the expansion of our Universe are discussed. The global solutions for the metric in the infinite extra dimension case are found; cosmological constraints are discussed. This is applied to various phenomenological aspects of brane worlds, i...