L-infinity

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In mathematics, ℓ ∞ {\displaystyle \ell ^{\infty }} , the (real or complex) vector space of bounded sequences with the supremum norm, and L ∞ = L ∞ ( X , Σ , μ ) {\displaystyle L^{\infty }=L^{\infty }(X,\Sigma ,\mu )} , the vector space of essentially bounded measurable functions with the essential supremum norm, are two closely related Banach spaces. In fact the former is a special case of the latter. As a Banach space they are, respectively, the continuous dual of the Banach spaces ℓ 1 {\displaystyle \ell _{1}} of absolutely summable sequences, and...

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