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Exact(10)
So making k → ∞, (3.4) yields the assertion.
This immediately yields the assertion by letting t → ∞ in the previous inequality.
end{aligned} Inserting this bound into (19) (which holds for arbitrary (v_{h})) yields the assertion.
Now summing over all facets (F_{T} inmathbb{F}_{T}) yields the assertion.
Thus, we have ∑ n = 2 ∞ d n | a n | r n − p < ( B − A ) a p, which, upon letting r → 1 −, readily yields the assertion (15).
So, ω φ λ 2 r ( f, t ) ≤ C ( h α + ( t h ) 2 r ω φ λ 2 r ( f, h ) ), which yields the assertion of Theorem 2 by the Berens-Lorentz lemma.
Similar(50)
Analogous argument yields the second assertion.
Applying the Chebyshev inequality yields the required assertion.
It yields the desired assertion (P(E_{i2}capOmega_{i2})=0) immediately.
It yields the desired assertion (mathbb{P}(J_{2}cap E_{2})=0) immediately.
To proceed, applying the Chebyshev inequality yields the required assertion.
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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