Homework assignment 2

Find an example of a random measure on a Euclidean space such that its intensity measure is the Lebesgue measure. Please avoid degenerate cases where the measure is in fact deterministic.

Please try determining the second moment measure \( M^{(2)} (A_1 \times A_2) \) for your particular random measure. It does not matter if you do not succeed, for some random measures this could be difficult or even impossible.