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Exact(25)
Let is bounded for each.
Since is bounded, is bounded for each.
(2) f is bounded for each (xinmathbb{R}^{m}). .
f is bounded for each (xinmathbb{R}^{m}).
(i) {x t } is bounded for each t ∈ 0, min 1, 1 τ.
Assume on the contrary that D u is bounded for each ( 1, u ) ∈ L ( P ) ∩ ( { 1 } × E ).
Similar(35)
Suppose that {T n x} is bounded for some x ∈ C. For each n ∈ ℕ, let x n := T n x.
(4) is bounded for.
which is bounded for fixed.
Since is bounded, for all.
This means that sequence is bounded for.
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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