Let be an open bounded subset of , assume we have a finite open covering of .
Consider the partition of unity subordinated: and where .
How does it follow that ?
Okay fair enough. I have another short question:
Since are real-valued functions, are vector fields according to my understanding of how the operator works.
In the book I am working from I am given that for it follows that has compact support and it follows then that
each has compact support? But is a vector field, does the notion of compact support extend to vector fields?
If so how?
Secondly it is stated that , but too is a vector field.
My understanding is that implies where is measurable and is bounded a.e..
Am I missing something? Thanks.