I am working through Alfen's proof that there exists a unique Haar measure on any locally compact group. There are a few propositions which have an unexplained notation which I am not familiar with - I think the notation is now outdated (the article is from 1963).
Alfsen, Erik M., A simplified constructive proof of the existence and uniqueness of Haar measure, Math. Scand. 12 (1963), 106-116 (1964). ZBL0274.43001.
In particular, I am not familiar with the notation $f_i^{\uparrow}f$ used in Corollary following Proposition 1.2 (page 108). What is the upward arrow meant to denote? It seems like notation to mean convergence, however I thought $f_i\rightarrow f$ would have been written then.
I am also not sure what is meant by $(f-1/n)^{+}$ in Proposition 2.3 (page 110). Does this simply mean the positively valued parts of $f-1/n$?
$f_n \uparrow f$ is common notation for "$f_n$ increases to $f$". That is, $(f_n)$ is a sequence of functions such that $f_1 \le f_2 \le f_3 \le \dots$, and $(f_n)$ converges to $f$. Usually this means pointwise convergence unless otherwise specified, and that makes sense in this context. An alternative notation for this is $f_n \nearrow f$.
Yes, $(f-1/n)^+$ means the positive part of the function $f-1/n$, i.e. $\max(f-1/n, 0)$.
I would say these are both still in widespread use and I wouldn't call them outdated.