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Let be a function such that (3.3).
Let φ : R + → R + be a function such that.
From now on, let be a function such that.
From now on, let be a function such that (2.17).
Also let be a function such that is increasing on, then (3.1).
Also let be a function such that is convex and increasing for.
From now on, let be a function such that and (2.4).
Let be fixed, and let be a function such that there exists an with for all.
Let (u(x)) be a function such that (u k)=a_{k}).
Let be a function such that there exists an with (2.1).
Let be arbitrary, and let be a function such that (3.11).
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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