grandes-ecoles 2011 Q11

grandes-ecoles · France · centrale-maths1__pc Proof Deduction or Consequence from Prior Results
Show that the "P-L" inequality $$\int_{-\infty}^{+\infty} h(x)\,dx \geq \left(\int_{-\infty}^{+\infty} f(x)\,dx\right)^{\lambda} \left(\int_{-\infty}^{+\infty} g(x)\,dx\right)^{1-\lambda}$$ is satisfied (if you choose to use the dominated convergence theorem then carefully verify that its conditions of validity are satisfied). 
Show that the "P-L" inequality
$$\int_{-\infty}^{+\infty} h(x)\,dx \geq \left(\int_{-\infty}^{+\infty} f(x)\,dx\right)^{\lambda} \left(\int_{-\infty}^{+\infty} g(x)\,dx\right)^{1-\lambda}$$
is satisfied (if you choose to use the dominated convergence theorem then carefully verify that its conditions of validity are satisfied).
Paper Questions
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17