(Functional analysis:)
A pair of real numbers p,q>1 satisfying 1/p+1/q=1.

Without motivation, this is completely idiotic. So here's some...

A version of Hölder's inequality with integrals immediately bounds the result of "applying" a function in Lq to a function in Lp. So any function in Lq is a linear functional on Lp: in symbols, Lq⊆(Lp)*. In fact, equality holds: Lq is the space of linear functionals on Lp (and, by symmetry, Lp is the space of linear functionals on Lq).

For p=1, we "have" q=∞. Except that this is of course not true, and the preceeding paragraph breaks down. It is still true that (L1)*=L, but the proof is somewhat different. And L is a completely different sort of space: typically, (L)*!=L1, but is much larger.

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