In this paper, we prove some fixed point theorems for condensing operators in the setting of Banach spaces via measure non-compactness, without using regularity. Our results improve and generalize many known literature.

The best-known version of Shelah’s celebrated singular cardinal compactness theorem states that if the cardinality of an abelian group is singular, and all its subgroups of lesser cardinality are free, then the group itself is free. The proof can be adapted to cover a number of analogous situations in the setting of non-abelian groups, modules, graph colorings, set transversals etc. We give a s...

In this paper we show that the well–known asymptotic efficiency bounds for full mixture models remain valid if individual sequences of nuisance parameters are considered. This is made precise both for some classes of random (i.i.d.) and non–random nuisance parameters. For the random case it is shown that superefficiency of the kind given by an example of Pfanzagl, [7], can happen only with low ...

We construct models containing exactly one supercompact cardinal in which level by level inequivalence between strong compactness and supercompactness holds. In each model, above the supercompact cardinal, there are finitely many strongly compact cardinals, and the strongly compact and measurable cardinals precisely coincide. Say that a model containing supercompact cardinals satisfies level by...