CardTowardMeasureProp\] For all $ k\in\mathbb{N} $, $ \theta_0,\ldots,\theta_k\in\mathbb {R} $ and all $ \tau_0,\ldots,\tau_k\geq0 $, one has $ \mathbb{P} \times\tilde{\mathbb{P} } $-almost surely that $$\frac{0}{n}\operatorname{card} \Biggl\{x\in\mathbb{Z}\