Example 2

Tag 085S, permanent. Cite it as [Bourbaki, Tag 085S].

The function $x^2$ is convex on $\mathbf{R}$ , since one has

\lambda x^2 + (1 - \lambda)(x')^2 - \left( \lambda x + (1 - \lambda)x' \right)^2 = \lambda(1 - \lambda)(x - x')^2 \geq 0

for $0 \leq \lambda \leq 1$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.

Nothing.