Cleanup
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@@ -7,10 +7,12 @@
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\[
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ab \le \frac{a^p}{p} + \frac{b^q}{q}
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\]
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and for any $\eps > 0$,
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\[
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ab \le \eps a^p + \frac{1}{q}(\eps q)^{-q/p}b^q
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\]
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\end{lemma}
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\begin{proof}
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Since $x \mapsto \exp(x)$ is convex,
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@@ -22,4 +24,5 @@
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\[
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ab = (\eps p)^{1/p}a \cdot \frac{b}{(\eps p)^{1/p}} \le \eps a^p + \frac{b^q}{q}(\eps p)^{-(1/p)q} = \eps a^p + \frac{1}{q}(\eps q)^{-q/p}b^q
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\]
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\end{proof}
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