What is meant by the notation lim_n?

Asked by bobbinhood (5898

) September 18th, 2011

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.

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2 Answers

I can confirm that the summation sigma with a subscript n means, “sum over the integer parameter n”—a kind of shorthand for the more formal n=1 to upper limit (or whatever). The starting value is inferred from context. Not sure about lim-sub-n. They used to joke about having lim sup as an appetizer

gasman (11345

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@gasman Thanks. I’ve seen the lone n underneath the sigma, but I’d never seen it as a subscript before.

“lim sup”. I like it. The other day, my husband said something about soup, and I just stared at him quizzically until I realized he was talking about “soup” and not “sup”. I felt a wee bit ridiculous given that he’s never even heard of sup.

bobbinhood (5898

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