ON AXIOMATIZATION OF THE CONCEPT OF MEASURABLE FUNCTION

Aleksander Rutkowski
1982 Demonstratio Mathematica  
This paper refers to [1] , where the problem of axiomatisatior. of the notion of random variable was investigated. The objects of examination were real-valued functions; the axioms were connected with elementary notions concerning reals: addition, multiplication, extraction, etc. Now we consider functions with values in an arbitrary poDisn space. Axioms have more set-theoretical character. We denote the set of all B-valued functions with a as a domain by ^B. We identify an integer n with the
more » ... of its predecessors jo,1,...,n-l|. It follows from the above that °2 is the set of all jo,l}-valued sequence of the length n, We denote 1>h. e set of all in'tegex's by go • X*6"t B^|«•« be subsets of a certain set X and let p e n 2. Write the Bet D B^1' by B where ien p B° = X -B and B 1 = B. It is easy to show that (cf. [2]) if n«m, pe n 2, q e m 2 then Bg £ Bp if <3 is an extension of p, Bq n-Bp = 0 otherwise. Moreover, for all integers n and k < n x = U{sp « P e n 2} and B k =
doi:10.1515/dema-1982-0413 fatcat:ndh74mnur5fv3doboidyimnwhi