What is meant by the notation lim_n?

I am studying Measure Theory by Donald Cohn, and he uses the notation lim_n (where _ denotes a subscript). Given the context, I am assuming this is a different way of writing the limit as n approaches infinity, but that is never specified. He also uses the notation Σ_n, which I assume refers to the sum as n goes from 1 to infinity.

Are you familiar with this notation? If so, am I correct in my interpretation of it? Is this notation still used, or is it no longer accepted? If it means what I think it does, it’s a convenient shorthand. I’m surprised I haven’t come across it before.