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In How does the Herglotz trick work?, is explained as in "Proofs from THE BOOK" by Aigner and Ziegler, but the "trick" itself I found to be not so clear.

The trick says:

It follows from $(4)$ that $h\left(\frac{x_0}{2}\right)+h\left(\frac{x_0+1}{2}\right)=2m$, and hence that $h\left(\frac{x_0}{2}\right)=m$.

But I can't understand why $h\left(\frac{x_0}{2}\right)=m$, that implies $h\left(\frac{x_0}{2}\right)=h\left(\frac{x_0+1}{2}\right)$, and I don't find anything that justifies this.

What am I missing?

Mohsen Shahriari
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Theennus
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1 Answers1

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Did $h$ have maximum value $m$? That would explain the implication I think.

user145337
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