Continuous additive function on the nonnegative real numbers
= Continuous additive function on the nonnegative real numbers
If $f:[0,\infty)\to\mathbb R$ is <continuous> and is an <additive function>, then $f(t)=tf(1)$. Additivity proves this first for nonnegative <rational numbers>; because $f$ is <continuous>, the identity extends to every nonnegative <real number>.