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Can someone explain the inequality? What property of concave functions is this using?enter image description here

rims
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    Please do not use pictures for critical portions of your post. Pictures may not be legible, cannot be searched and are not view-able to some, such as those who use screen readers. – Martin R Apr 08 '21 at 09:27
  • I am the downvoter. The reasons are in Martin's comment. – Giuseppe Negro Apr 09 '21 at 05:14

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Non-negative concave functions are subadditive, see for example Concave implies subadditive: $$ f(t+\tau) \le f(t) + f(\tau) \, . $$ For the estimate in the other direction use that $g(t) = f(1-t)$ is also concave: $$ f(t) = g(1-t) \le g(1-t-\tau) + g(\tau) = f(t+\tau) + f(1-\tau) \, . $$

Martin R
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