[Merged by Bors] - feat(analysis/mean_inequalities): Hölder's inequality for infinite sums #11314
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hrmacbeth
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RemyDegenne
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| summable (λ i, f i * g i) ∧ | ||
| ∑' i, f i * g i ≤ (∑' i, (f i) ^ p) ^ (1 / p) * (∑' i, (g i) ^ q) ^ (1 / q) := |
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It would be nice to have two more lemmas which each give one of the terms in this conjunction: one for summable, the other for tsum. Since the proof of both parts is the same, I don't suggest that you break this theorem in two, but rather that you keep this one and add two corollaries.
Same thing for the other summable (...) ∧ ... theorems
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LGTM |
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State a few versions of Hölder's inequality for infinite sums.
The specific forms of the inequality chosen are parallel to those for Minkowski's inequality in #10984.