In one way or another, Holder's theorem underlies the various theories of extensive measurement that are designed to account for the existence of such numerical measures as mass, length, and time. In order to study more complicated numerical measures such as those arising in aerodynamics, it is necessary to generalize Holder's theorem. This study presents a result that improves on a result due to Giles, gives a natural quantitative representation of thermodynamics, and has, as a special case, a nice formulation of necessary and sufficient conditions for traditional extensive measurement. 26 pp. Refs.
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