id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
work_pqhgcn6fnvbfndrtonjsx3spki	R. Duncan Luce	A "Fundamental" Axiomatization of Multiplicative Power Relations among Three Variables	1965	9	.pdf	application/pdf	3841	430	83	ordered b y a relation that satisfies the axioms o f conjoint measurement. satisfies the axioms o f extensive measurement. the axioms of extensive measurement hold for each of these components scparately, and that a new axiom relates the two measurement systems. three of the four axioms of conjoint measurement are: final axiom of conjoint measurement, we need: T h e Archimedean axiom for conjoint measurement is: Note that Axiom F is needed to state it since im is a rational when i is an integer and Let m and n be the integers whose existence is asserted in Axiom C-E. Theorem 2 are sufficient to show that there exists a positive real-valued function v, T h e principal theorem shows that when Axioms C-E and F hold the functions From the conjoint measurement representation applied to Axiom C-E, we First, observe that there exists a positive real-valued function f on the rationals 	./cache/work_pqhgcn6fnvbfndrtonjsx3spki.pdf	./txt/work_pqhgcn6fnvbfndrtonjsx3spki.txt