I am reading the article "Polygonal Approximations of Solutions of the Initial Value Problem for a Conservation Law" by Dafermos, Journal of Math. Analysis and Applications 38 (1972), pp.33-41.
At p.38, there is a reference to a type of convergence I do not know. In particular it is written that $u(x,t)\to u(x,T)$ , $t\to T$ essentially in $(-\infty,\infty)$.
What does it mean? Can you explain it to me or at least give a reference? Many thanks.