Measurability of the geometric measure for a level set of a random function. (Russian) Zbl 0589.60043

Radchenko, A. N.

Teor. Veroyatn. Mat. Stat. 31, 116-125 (1984).

Let X,Y be metric spaces and \(\xi\) :\(\Omega\) \(\times X\to Y\) a random function. Conditions for the measurability of \(G\{x\in T\subset X:\quad \xi (x,w)=y\}\) are given, where G(\(\cdot)\) is some geometric measure. G(\(\cdot)\) is a generalized spherical Hausdorff measure.

Reviewer: N.Leonenko

MSC:

60G60	Random fields
60D05	Geometric probability and stochastic geometry
60G57	Random measures
60G05	Foundations of stochastic processes

Keywords:

geometric measure; random set; measurability; spherical Hausdorff measure