I have no idea how to prove that the space $X$ of all integrable functions on the interval $[0,1]$, for $f,g\in X$, with the following metric:
$$\rho(f,g)=\int|f(x)−g(x)|~dx$$
is separable. I'll appreciate any help, please. Thank you
I have no idea how to prove that the space $X$ of all integrable functions on the interval $[0,1]$, for $f,g\in X$, with the following metric:
$$\rho(f,g)=\int|f(x)−g(x)|~dx$$
is separable. I'll appreciate any help, please. Thank you