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Reference.org
Metric lattice
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<p>In the mathematical <a href="/facts/Order_theory/gn6fM3oJ">study of order</a>, a metric lattice L is a <a href="/facts/Lattice_(order)/5ak6ufky">lattice</a> that admits a positive valuation: a function <i>v</i> ∈ <i>L</i> → ℝ satisfying, for any <i>a</i>, <i>b</i> ∈ <i>L</i>, v ( a ) + v ( b ) = v ( a ∧ b ) + v ( a ∨ b ) {\displaystyle v(a)+v(b)=v(a\wedge b)+v(a\vee b)} and a > b ⇒ v ( a ) > v ( b ) . {\displaystyle {a>b}\Rightarrow v(a)>v(b){\text{.}}} </p>