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Taking (tilde{h}_{2}=varepsilontilde{h}_{1}), we complete the assertion (3).
Taking (delta=l_{3}varepsilon) and (tilde{h}_{3}=(1+varepsilon )tilde{h}_{2}), we complete the assertion (4).
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According to our claim, we get T u ∈ L, which completes the assertion.
Therefore (Sigma_{mu}^{u}), (Sigma_{mu}^{v}) and (Sigma_{mu}^{w}) must be three zero-measure sets, which completes the assertion of Step 1. Step 2: We will continuously move the plane (x_{1}=mu) to the right as long as (2.4) holds.
This estimate completes the proof of assertion (2.3).
By the Banach-Steinhaus theorem ({|a x,T_{k} u_{n}), DT_{k} u_{n}))| _{bar{M}}}_{n}) is bounded; this completes the proof of assertion (1).
This completes the proof of the assertion.
If f ≥ 0, then ψ ≥ 0 and consequently x ≥ 0. Reference to (2.5) completes the proof of the assertion (1).
By (i), (zin A z)) which is contradicted by (ii), and this completes the proof of the assertion.
Now reference to Theorem 5.1 completes the proof of the assertions (1) and (2) of Theorem 3.2.
She even sounded skeptical at my assertion that we had completed the whole package.
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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