2 Approaches in index theory 47
47 Chapter 2 Approaches in Index theory in this chapter an attempt is made to present an overview of theories or "approaches" in index theory along with some Index formulas (some of them, however, failed in gaining importance in the practice of official price statistics).1 There is no end to the search for more general Index functions or in attempts to derive classes of index functions an the basis of some few fundamental principles or some new ways of look- ing at the Index problem. Thus the chapter can necessarily present only fragments of more or less theoretical nature. 2.1 Outline of Index theories or "approaches" Index theory has a wide variety of "approaches" to offer. For the most part Index the- ory, and hence also the rivalling approaches, have to do with the assessment of in- dex formulas, lt is perhaps a fruitless effort to count all the different index formulas that have been invented and proposed by anybody, as being the "best" or "ultimate" formula. There are hundreds of formulas and the set of formulas we might think of being useful in some respect is unbounded. Introducing this chapter, therefore, the best we can do is to try to give a systematic, fair, and balanced overview. Reviewing textbooks on index theory and price statistics, a salient feature of most of them is that often some "approaches" are exempted from presentation, or that at least the place devoted to some topics may appear to be too small as...
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