I have a question about Flow Decomposition Theorem.
In the theorem say that a flow $f$ can be decompose in $k$ flows, $f_1, f_2 ... f_k$, and the cost of the flow $f$ is equal to the sum of the costs of the flows $f_i$.
My concern is not to messing up the cost of a flow with the value of a flow.
So, I want to know if is correct how I write the formula for this property: $$f = \sum_{i=1}^{k} f_i$$