The Furstenberg set and its random version
The Furstenberg set and its random version
We study some number-theoretic, ergodic and harmonic analysis properties of the Furstenberg set of integers S={\{2^{j}3^{k}\}} and compare them to those of its random analogue T . In this half-expository work, we show for example that S is “Khinchin distributed”, is far from being Hartman uniformly distributed while T is, …