: Mathématiques: Banach lattice

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Banach lattice

In the mathematical disciplines of in functional analysis and order theory, a Banach lattice $(X,‖\cdot‖)$ is a complete normed vector space with a lattice order, such that for all $x, y \in X$ , the implication ${\\displaystyle {|x|\\leq |y|}\\Rightarrow {\\|x\\|\\leq \\|y\\|}}$ holds, where the absolute value $|\cdot|$ is defined as ${\\displaystyle |x|=x\\vee -x{\ ext{.}}}$
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Banach_lattice)

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