EDB β€” 1C3

↑ ← β†’ ↓ view in whole PDF view in whole HTML

View

English

E29

[1C3]Difficulty:*.Let \(f:[0,1]→ℝ\) be Riemann integrable and \(πœ‘:ℝ→ℝ\) convex: show that

\begin{equation} \label{eq:dis_ Jensen} πœ‘\left( ∫_ 0^ 1f(x))\, {\mathbb {d}}x\right) ≀ ∫_ 0^ 1πœ‘(f(x))\, {\mathbb {d}}x \quad . \end{equation}
30

This result is known as Jensen’s inequality.

Download PDF
Bibliography
Book index
  • function, Riemann integrable ---
  • Riemann integral
  • Jensen inequality
  • inequality, Jensen β€”
Managing blob in: Multiple languages
This content is available in: Italian English