Meaning of $S^{I}$

Question

I have a measurable space $(S, \Sigma) $ and an index set I. What does it mean by $S^I$. Can someone explain with the help of an example? I am studying stochastic processes and found this in the definition of Path space.

Answer 1

It is the space (or simply the set) of maps $I\to S$. Another way of saying the same thing in the case $I$ is countable is the set of sequences of elements of $S$ indexed by $I$, since any map $I\to S$ determines a sequence given by the images and any sequence indexed by $I$ determines the image of a map $I\to S$.

Answer 2

In the simplest language possible: $S^I$ is the set of all functions from $I$ to $S$.

This avoids the possibly confusing term "space".