Subscript before a function symbol?

Question

Does anyone know what the subscript before the function means? $$ _pf_p $$

It's part of a definition for selfish routing in networks:

Let $N = (V,E)$ be the network, which is a directed graph. There are $k$ source-destination paris $\{{s_1}, {t_1}\}, ..., \{{s_k}, {t_k}\}$. ${P_i}$ = the set of paths from ${s_i}$ to ${t_i}$ and $P = \cup_iP_i$. The flow $f: P \rightarrow R^+$, where $P$ is negligible traffic and $R^+$ represents a flow. The load of edge $e$ is $f_e = \sum_{p\in P}$ such that $e$ is in $_pf_p$.

Also, am I right in thinking this means the union of all possible paths? $$P = \cup_iP_i$$

Thanks!

Answer 1

"The load of edge $e$ is $f_e = \sum_{p\in P}$ such that $e$ is in $_pf_p$" should be: $$f_e = \sum_{p\in P \text{ such that }e\text{ is in }p} f_p$$