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Definition 5

Notes:

The formal definition of the digitization run on each digitization level. Run_k means ”run of runs of runs...” with the word ”runs” repeated k times (one time in singular and k-1 times in plural). Here you can see very clearly the first intuitive idea that the object of a given level is the element on the next levels. We define the runs as SETS with runs of the lower level as elements.

Pay also attention to the t-function: this one uses the Sum-function which decides about the first on the level.