We describe how the notion of positivity relates to the other properties.
How are these two optimality notions related? In general, they are not.
This is where the notion of an upper gradient comes in.
There is a fourth notion of phantom map which bears the same relation to the third definition as the first does to the second.
Our notion of nonanalytic integral encompasses such well known examples as......
More specialized notions from Banach space theory will be introduced as needed.
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