Random compact set meets the graph of nonrandom continuous function

TL;DR

This paper demonstrates that random compact sets in the plane almost surely intersect the graphs of continuous functions, impacting the factorization properties of black noise over the plane.

Contribution

It establishes a probabilistic intersection property between random compact sets and continuous function graphs, revealing limitations in noise factorization.

Findings

Random compact sets almost surely intersect continuous function graphs.

Black noise over the plane cannot be factorized when split by such graphs.

The result links geometric properties of random sets to noise theory.

Abstract

On the plane, every random compact set with almost surely uncountable first projection intersects with a high probability the graph of some continuous function. Implication: every black noise over the plane fails to factorize when the plane is split by such graph.