Let $E$ be the set of continuous functions $f$ from $I$ to $\mathbb{R}$ such that $f^2 w$ is integrable on $I$. Show that $E$ is an $\mathbb{R}$-vector space.
Let $E$ be the set of continuous functions $f$ from $I$ to $\mathbb{R}$ such that $f^2 w$ is integrable on $I$.
Show that $E$ is an $\mathbb{R}$-vector space.