# Analysis Notation Question

1. Nov 14, 2014

### nateHI

The context is Tonelli/Fubini.

What's the difference between saying
$y\mapsto\int_Ef^y(x)dx$ is measurable
and
$\int_Ef^y(x)dx$ is measurable

2. Nov 14, 2014

### mathman

There really isn't any. All the first statement is doing is emphasizing the fact that the integral is a measurable function of y.

3. Nov 15, 2014

### Fredrik

Staff Emeritus
The second statement is a lazy version of the first. It's like saying that $x^2$ is differentiable instead of saying that $x\mapsto x^2$ is differentiable.

4. Dec 2, 2014

OK thanks!