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On Order Invariant Synthesizing Functions

✍ Scribed by Jean-Luc Marichal

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
143 KB
Volume
46
Category
Article
ISSN
0022-2496

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✦ Synopsis

This paper gives a description of the class of continuous functions that are comparison meaningful in the sense of measurement theory. When idempotency is assumed, this class reduces to the Boolean max-min functions (lattice polynomials). In that case, continuity can be replaced by increasing monotonicity, provided the range of variables is open. The particular cases of order statistics and projection functions are also studied.

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In this paper the rearrangement-invariant hulls and kernels of the classes loc ] on a noncompact nondiscrete locally compact abelian group are characterized. The space L 1 loc & S$ of tempered distributions serves as the extended domain of the Fourier transform instead of the classical domain L 1 +