1,662
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m (→Theorem) 
(→Application: B.L.T. to BLT, to match the other appearance of this acronym.) 

<math>\mathsf{I}</math> as a function is a bounded linear transformation from <math>\mathcal{S}</math> into <math>\mathbb{R}</math>.<ref>Here, <math>\mathbb{R}</math> is also a normed vector space; <math>\mathbb{R}</math> is a vector space because it satisfies all of the [[vector space#Formal_definitionvector space axioms]] and is normed by the [[absolute valueabsolute value function]].</ref>
Let <math>\mathcal{PC}</math> denote the space of bounded, [[piecewise]] continuous functions on <math>[a,b]</math> that are continuous from the right, along with the <math>L^\infty</math> norm. The space <math>\mathcal{S}</math> is dense in <math>\mathcal{PC}</math>, so we can apply the
==The Hahn–Banach theorem==
