For fixed (v>0), show that the Matrn measures are mutually consistent in the sense that (M_{d+1}(A times

For fixed \(v>0\), show that the Matérn measures are mutually consistent in the sense that \(M_{d+1}(A \times \mathbb{R})=M_{d}(A)\) for all \(d \geq 0\) and subsets \(A \subset \mathbb{R}^{d}\). In other words, show that \(M_{d}\) is the marginal distribution of \(M_{d+1}\) after integrating out the last component. For \(v>-1\), show that the Matérn measures are mutually consistent in the sense that \(M_{d+1}(A \times \mathbb{R})=M_{d}(A)\) for all \(d \geq 2\).