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I am currently reading Rick "Durrett's Probability: Theory and Examples", and I am confused by his notation what does mean $\inf_n X_n$ or $\liminf_n X_n$ where $\{X_n\}$ is a sequence of random variables (th 1.3.5 p14) ? Random variables are measurable functions -- what is the infinitum of a sequence of functions ?
Note, convergence is defined exactly after this theorem.
He certainly consider the pointwise infimum of $\liminf$, that is, for any $\omega\in \Omega$, $\left( \inf_n X_n\right) \left(\omega\right)$ denotes the infimum of the sequence $\left(X_n\left(\omega\right)\right)_{n\geqslant 1}$ and $\left( \liminf_nX_n\right) \left(\omega\right)$ denotes the $\liminf$ of the sequence $\left(X_n\left(\omega\right)\right)_{n\geqslant 1}$.
