What is the meaning of measure valued function?

Question

Are the term measure valued function is same as measurable function or it is a function which gives measure for every element in the domain of this function? Can someone provide one example of measure valued function?

Answer 1

For each real number $x$ define $\mu_x(E)=\mu(E+x)$ where $\mu$ is some fixed measure. Then the function $F(x)=\mu_x$ is a measure valued function on $\mathbb R$.

Answer 2

I can't tell for your original source. In English, measure-valued function means a function that ranges in the set of measures (presumably) over some fixed space, much like what happens in statistical models, or when you consider the diverse possible convergences of sequences of measures. Therefore, there should be no reason to assume otherwise.