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Then statement (iii) is implied by statements (i) and (ii).
The statements (i), (ii) are consequences of [18, Lemma 2.5].
There hold the following statements: (i), (ii If for all then.
Then by Theorem 5, we obtain the statements (i) and (ii).
3.8 that statements (i) and (ii) of Theorem 3.3.3 do not hold for (p<2).
Statements (i) and (ii) also hold if we reverse the signs in all of the inequalities.
Consider the following statements: (i) The family ((f_{u_{1}}, g_{u_{2}}; A ;U)) satisfies the ((AFRC)).
Noting that statements (i) and (ii) hold followed by (iii)–(v), we will only prove conclusions (iii)–(v).
Consider the following statements: (i) (gin operatorname{wuCs}(X^)). (ii) (Swidehat{F}_{w^(g)=ell_{infty }(widehat{F})).
Open image in new window (8)With Statements (i), (ii), (iii), (iv) and (v) at hand we can now prove the required result.
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By using the package Mathematica, one can see that the statements (i - vi) are true.
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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