In a book on statistics I saw the notation $x^n=(x_1,\dotsc,x_n)$ and wondering how common this is in measure theory/statistics.
More precisely it is about a probability space $(\mathbb{H},\mathcal{H},P) = (\times_{i=1}^\infty\mathbb{H}_i,\otimes_{i=1}^\infty\mathcal{H}_i,\otimes_{i=1}^\infty P_i)$ and $x=(x_1,x_2,...) \in \mathbb{H}$. The random variables $X_i: \mathbb{H} \to \mathbb{H}_i$ are defined as $X_i(x) = x_i$.
Now $X^n := (X_1,\dotsc,X_n)$ and $X^n(x) = x^n=(x_1,\dotsc,x_n)$.
Can this notation be used in a publication in statistics?