\begin{definition}[Definition:Probability Limit/Lower]
Let $T$ be a time series.
Let $S$ denote the range of $T$.
Let $L$ denote the set of lead times of $T$.
Let $\hat z_t$ be a forecast function on $L$.
Let $\map {\hat z_t} l$ denote the forecast value of the observation at the timestamp of lead time $l$.
Let $\Delta_p$ be a probability limit for $\map {\hat z_t} l$.
The '''lower probability limit''' of $\map {\hat z_t} l$ is the value $\map {\hat z_t} l - \Delta_p$.
\end{definition}