Finite soluble groups by Klaus Doerk; Trevor O Hawkes

By Klaus Doerk; Trevor O Hawkes

Show description

Read Online or Download Finite soluble groups PDF

Similar abstract books

Intégration: Chapitres 7 et 8

Intégration, Chapitres 7 et 8Les Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements. Ce quantity du Livre d’Intégration, sixième Livre du traité, traite de l’intégration sur les groupes localement compacts et de ses functions.

Extra info for Finite soluble groups

Example text

To see this, consider in the case Ω = [0, 1] the sequences xn = π2 (4n + 1)χDn , yn = π2 (4n − 1)χDn (n = 1, 2, . . ), where Dn are subsets 1 , and in the case Ω = N the sequences xn = 2n+1 χ{n} , yn = of [0, 1] with λ(Dn ) = 2πn 2n 2n−1 χ{n} (n = 1, 2, . . ). Obviously, these sequences are bounded and satisfy the condition 2n lim xn − yn = 0; on the other hand, the sequence F xn − F yn is bounded away from n→∞ zero, and hence F cannot be uniformly continuous on bounded sets. 7. 9. Let X and Y be two ideal spaces, and let f be a Caratheodory function.

Vajnberg [78], [164], [165], [238-241], [341346]; in the last mentioned paper, the superpo- sition operator is called "Nemytskij operator"for the first time. P. Zabrejko. 9) characterizes the superposition operator, or if there are other operators which are locally determined. 6) is the only locally determined operator on the space S (over a separable measure): in fact, since the space S has the cardinality of the continuum, its elements can be indexed by the ordinals from 1 to ω, the first uncountable ordinal.

24 Chapter 2 The superposition operator in ideal spaces In this chapter we are concerned with the basic properties of the superposition operator in so-called ideal spaces which are, roughly speaking, Banach spaces of measurable functions with monotone norm. To formulate our results in a sufficiently general framework, we must introduce a large number of auxiliary notions which will be justified by the results in concrete function spaces given in subsequent chapters; we request the reader’s indulgence until then.

Download PDF sample

Rated 4.17 of 5 – based on 44 votes