I'm looking for a definition for a particular function(-input) property. Considering a function $f$ that takes as input a list of elements and produces in output just one element, which is the property that says that the result of $f$ for a given list of elements is EQUAL to the result of the same function $f$ that takes as input a list of elements which are the results of $f$ on subset to the given list?

I provide here some example because I understand the description is quite messy: Given the list [1,2,3,4,5] the first two examples abide by the property meanwhile the third does not:

$max([1,2,3,4,5]) = 5 = max([max([1,2]),max([3,4,5])])$ $avg([1,2,3,4,5]) = 3 = avg([avg([1,2]),avg([3]),avg([4,5])])$ $avg([1,2,3,4,5]) = 3 \neq 2,75 = avg([avg([1,2]),avg([3,4,5])])$

Personally, I think is a sort of functions associativity and I think the second case is just a fortuitous one.


Properties like the one described in the OP are studied in the context of aggregation functions (I refer, in particular to pag.32-33 and pag.34 for decomposability). As motivating example, I would consider means, generalized means and the celebrated quasi-arithmetic or Kolmogorov-Nagumo means.

  • $\begingroup$ Thanks, right what I was looking for! $\endgroup$ – Nicola Sep 9 '14 at 14:11
  • $\begingroup$ You are welcome :) The book is quite nice. It contains many examples coming from applications, like copulae. $\endgroup$ – Avitus Sep 9 '14 at 14:15

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.