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It is easily seen that (2.27).
It is easily seen that is monotone.
Now by letting (1.8). it is easily seen that (1.9).
from which it can be easily seen that (2.18).
By noting that (2.10), it is easily seen that (2.20).
It is easily seen that is a solution of (1.2).
It is easily seen that is continuous on.
From (3.12), it is easily seen that (3.16) holds as.
By noting (2.12), it is easily seen that (2.22).
It is easily seen that is open and convex valued.
From (F) and using the Hölder inequality, it is easily seen that (3.5).
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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