I'm reading a proof by G. Cybenko, and I'm stuck on one step as follows:
Let $F$ be a linear form satisfying $F(h)=\int_{I_{n}}h(y^Tx)\,d\mu(x)$, where $y$ is fixed, $\mu$ is some regular Borel measure, $h$ is a bounded measurable function, and $I_{n}$ is the n-dimensional unit cube, $[0,1]^n$.
Let $s(u)=\sin(m*u)$ and $c(u)=\cos(m*u)$.
Why does $F(s+ic)=\int_{I_{n}}\cos(m^Tx)+i\sin(m^Tx)\,d\mu(x)$?
I feel like this is a trivial hang-up.
Thanks in advance.
It seems that the author has made a typo, where he meant to write
$F(c+is)=\int_{I_{n}}\cos(m^Tx)+i\sin(m^Tx)\,d\mu(x)$.