Integrand of a definite integral

Question

If we have an integral $\int_A f(x)dx$, or what I am more specifically interested in, $\int_A fd\mu$ where $\mu$ is a measure, is the integrand $f$ or is it $f$ on the domain $A$, where A is some set (say of real numbers).

Answer 1

I think you could describe $\int_{A}f\text{d}\mu$, where $f$ is a $\mu$-measurable function and $A$ a $\mu$-measurable set on which $f$ is definite, as follows:

$\int_{A}f\,\text{d}\mu$ is "the integral of $f$ on $A$ with respect to the measure $\mu$, where $f$ is called the integrand of this integral", so that the term "integrand" explicitly depends on a particular integral and it is not useful to say that the integrand is $f$ restricted to $A$ because the integral already contains this information.