So I'm trying to study som Markov Chains. And I've stumbled across "The Renewal Reward Theorem" or "The elementary renewal theorem", it seems to have different names. The theorem basically says:
$lim_{t\to \infty} \frac{1}{t} m(t) = \frac{1}{E(S_1)}$
I'm trying to find a intuitive way to understand this. $m(t)$ can be interpreted as "# customers that came to the store during time $t$". And $\frac{1}{t} m(t)$ to be like "Every time $t$ so many peoples arrive". But I don't know what to think if the right and side and limit of the expression.
Thanks if you can give a nice simple example of this :)