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Since, there exists a compact set such that for.
Then there exists a compact absorbing set (KsubsetGamma) [30].
There exists a compact subinterval of, and such that (110).
Then, there exists a compact upper convexifactor of f at x.
Since is a compact mapping, there exists a compact subset of such that.
Let be a locally Lipschitz function such that there exists a compact with for a.e.
Assume that is nonexpansive and there exists a compact subset of with.
(i for each, there exists a compact -subspace of containing such that for each.
Then there exists a compact and continuous embedding (Xhookrightarrow L^{r(cdot)}(partialOmega) ).
Suppose there exists a compact subset C in E such that.
For any and, we claim that there exists a compact subset of such that.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com