Possible Duplicate:
Are measurable functions closed under addition and multiplication, but not composition?
Let $\varphi: \mathbb{R}\to \mathbb{R}$ and $f$ is a real-valued measurable function. If $\varphi$ is continuous then I can show that $\varphi \circ f$ is measurable. Is the conclusion still true if we only know the $\varphi$ is Lebesgue measurable?