If $I$ is any set of indexes, we define $E^I=\{(x_i)_{i\in I}:x_i\in E\,\,\forall i\in I\}$, $E$ being any set. Subsets of $E^I$ of the form $C_J=\{x_i\in B_i\,\,\forall i\in J\}$, where $B_i\in\mathcal{A}\,\,\forall i\in J$, $\mathcal{A}$ is a $\sigma$-algebra on $E$ and $J\subseteq I$ is finite, are called "cylinder sets", and form a basis of the product $\sigma$-algebra $\mathcal{A}^{\otimes I}$. Why are these sets called "cylinder sets"? What is the origin of this name?
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