Let be Lebesgue integrable functions on the real line R and let , .
Show that is measurable on R.
i dont even know how to start. help is appreciated so much.
Start by showing that the function is measurable (for fixed x). You should be able to do that from the definition of measurability. You then need to show that the product of that function with g is measurable. To show that the product of two measurable functions is measurable, first show (from the definition) that if is measurable then so is . Then, if and are measurable, so is .