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would be the right continuity of the process ({mathcal {E}}(f)), because of (40).
Then all the assumptions of Proposition 8 except the right continuity of θ are satisfied.
Of course, concerning norm continuity or differentiability at we only mean right continuity or right differentiability.
From the right continuity of φ, there exists δ > 0 such that φ + θ.
From the right continuity of θ, there exists (delta> 0) such that (theta varepsilon+ delta) < theta varepsilon) + alpha).
In our new proof, the reason why we need the right continuity of θ is quite clear.
Similar(40)
In fact, since φ ∈ ( Φ 0 ) or , by the right-continuity of φ, we know that F 1 satisfies condition (A-1).
We conclude by providing the following result fromBiagini and Zhang (2017), which shows sufficient conditions for having right-continuity of the sublinear operator.
In this section, (mathbb {F}=left (mathcal {F}_{t}right)_{tgeq 0}) denotes a filtration satisfying the usual hypothesis of right-continuity and completeness.
Then we could talk about ( T, g, M ) -right-Picard sequences, ℳ-right-continuity, ( O, M ) -right-compatibility and right-regularity.
By the same token, the upper semicontinuity of a non-decreasing function F : [ 0, 1 ] × [ 0, 1 ] → [ 0, 1 ] is equivalent to its right-continuity in each component.
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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