grandes-ecoles 2012 QI.C

grandes-ecoles · France · centrale-maths1__psi Sequences and Series Uniform or Pointwise Convergence of Function Series/Sequences

Show that if $E$ is not empty, then $Lf$ is continuous on $E$, where for $x \in E^{\prime}$, $$Lf(x) = \int_0^{+\infty} f(t)e^{-\lambda(t)x}\,dt.$$

Show that if $E$ is not empty, then $Lf$ is continuous on $E$, where for $x \in E^{\prime}$,
$$Lf(x) = \int_0^{+\infty} f(t)e^{-\lambda(t)x}\,dt.$$