I want to understand the difference between Independent, Pairwise Independent and Mutually Independent events. I have read multiple answers related to this like in here, here and here. Most of them talk with 3 events and explain the difference between pairwise independent and mutually independent. I understand that. But what happens when there are $n$ events?
Suppose, $A_1$, $A_2$,....$A_n$ are n events, if
$$P(A_1 \cap A_2 \cap .... A_n) = P(A_1)P(A_2)....P(A_n)$$ but they are neither pairwise independent nor mutually independent. Only the above statement holds. Now, are these events still called Independent Events? Or is there any separate nomenclature for that?