An indexed family of filters and their elements

Question

Let $X$ is an indexed (by some set $n$) family of filters (on some poset $\mathfrak{A}$).

Is there any standard notation/terminology for the set $\{ y\in \mathfrak{A}^n \,|\, \forall i\in n:y_i\in X_i \}$ or its elements?

Answer 1

I thought on this question long time but realized that it is trivial only now after posting my question to math.SE. Maybe telepathy with readers of my question and/or spirit has helped me.

$$\{ y\in \mathfrak{A}^n \,|\, \forall i\in n:y_i\in X_i \} = \prod X.$$