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Given the character:lambda] weightings can vary, there is considerable flexibility in the family of admissible measures.
Admissible measures of diversity allow specification of the number of types (species, alleles, etc).
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Consider a p-admissible vector measure (mu ).
Let (1le padmissible vector measure.
(Heuristic definition) Let us consider (1le p< infty ) and a p-admissible vector measure (mu =(mu _0,ldots,mu _k)) in (mathbb {R}).
end{aligned}Let us consider the projection (P ,W^{k,p}(Delta,mu )longrightarrow prod _{j=0}^k L^{p}(Delta,mu _j)), given by (Pf= f,f',ldots,f^{ k)})). Let (1le padmissible vector measure.
For each (1le padmissible vector measure (mu ) in (mathbb {R}), consider the Banach space (prod _{j=0}^k L^{p}(Delta,mu _j)) with the norm begin{aligned} Vert fVert _{prod _{j=0}^k L^{p}(Delta,mu _j)} = left( sum _{j=0}^k left| f_jright| _{L^{p}(mu _j)}^p right) ^{1/p} end{aligned}for every (f=(f_0,ldotsdots,f_k)in prod _{j=0}^k L^{p}(Delta,mu _j)).
As in forensic assessment, the Type II Error (classification of malingered injury as real) is not admissible; the psychometric measure is not sufficient evidence of psychological injury.
Assume that u is such that U is admissible and the measure w ( t ) d t is non-degenerate with respect to U q p. (i) Let 1 ≤ q < ∞.
Assume that u is such that U is admissible and the measure w ( t ) d t is non-degenerate with respect to U q. (i) Let 0 < p ≤ 1, p ≤ q < ∞.
Assume that u is such that U is admissible and the measure w ( t ) d t is non-degenerate with respect to U q p. Let { x k } be any discretizing sequence for φ defined by (3.3).
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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