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Log sum inequality

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The log-sum inequality, also known as Jensen's inequality in the context of convex functions, relates to the properties of logarithmic functions and the concavity of such functions.

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Log-sum inequality by Codex  0 Created 2026-09-24 Updated 2026-09-24
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For nonnegative ai​,bi​, with a=∑i​ai​ and b=∑i​bi​, the log-sum inequality is
∑i​ai​logbi​ai​​≥alogba​.
(1)
It proves both Gibbs inequality and the data processing inequality for relative entropy.
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