Random selection of Borel sets II

Bernd Günther
2013 Applied General Topology  
The theory of random Borel sets as presented in part I of this paper is developed further. Special attention is payed to the reconstruction of the topology of the underlying space from our presentation of the measure algebra, to an analysis of capacities in context of random Borel sets, to inspection processes on the unit segment and to the Markov process of random allocation. 2010 MSC: Primary 60D05; Secondary 54H05 Proposition 2.1. If a type I resolution is used for the isomorphism theorem
more » ... morphism theorem [2, Thm.6.1], then: i) The Borel set corresponding to a sequence (x nm ) can be chosen as open if and only if x nm ϕg dμ as we please (cf. [2, Thm.6.1]). If the element (x nm ) 0≤m<2 n ,n∈N0 ∈ Y represents a closed set A containing A, then x nm ≥ x nm > 0 for all m, n, and remark 2.2 implies 0 = lim N →∞ 2 n−N 2 N −n m≤k<2 N −n+1 m (1 − x Nk ) = 1 − x nm for all
doi:10.4995/agt.2012.1639 fatcat:2acedj73grf43cd4ykid4wp2eq