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V ( A ) is non-empty and closed subset of R | A |, For each k ∈ A, there is a V k ∈ R, such that V ({k}) = (-∞,V k ], V ( A ) is comprehensive, i.e., for all x ∈ V ( A ) and for all y ∈ R | A |, if y [ k ] ≤ x [ k ] ∀ k ∈ A, then y ∈ V ( A ), The set V ( A ) ⋂ y ∈ R | A | ∣ y [ k ] ≥ V k ∀ k ∈ A is bounded.
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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