Chapter 5

Random Variability

Suppose T is a finite or infinite labeling set. For the purposes of this book the domain RT is structured by means of a number of features:

  • points x = xT;
  • cells I = I[N] Image I(RT);
  • figures E Image E(RT);
  • point-cell association x Image I[N]* and I[N] Image x*;
  • partitions Image, divisions Image, gauges γ;
  • integral Image h, and variation Vh, defined for functions h(x, N, I) of associated triples (x, N, I[N]).

A real- or complex-valued function F defined on the figures E(RT) of RT is an additive (or Stieltjes) cell function if F is finitely additive on disjoint figures. A Stieltjes cell function F is a distribution function or potentiality distribution function if F(RT) = 1. Every Stieltjes cell function is integrable (in the Stieltjes-complete or Henstock sense) on figures.

If an experiment (measurement ...

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