Question about alternate subset notation

Question

I am reading a new text, and I have come across the notation '$\Subset$' as well as '$\subset$'. Am I correct in assuming that '$\Subset$' is an alternative method of specifying an improper subset like the usual '$\subseteq$'?

Answer 1

The symbol has no standard meaning. It is up to each author who uses it to supply a definition and explanation of what he uses it to mean, early enough to avoid confusing the reader.

Answer 2

After scanning through the end pages more carefully, I found embarrassingly that I missed the answer the first time I looked! In this context (locally integrable functions under Lebesgue measure), the symbol was used to represent a subset whose closure is compact and is also a subset.