Section Measures
Why
Toward a theory of iterated integrals, we need to know the function measuring a section is integrable.
Results
Let $(X, \mathcal{A} , \mu )$ and $(Y,
\mathcal{B} , \nu )$ be sigma-finite measurable
spaces.
Let $E \in \mathcal{A} \times \mathcal{B} $.
The function $x \mapsto \nu (E_x)$ is
$\mathcal{A} $-measurable and the function $y
\mapsto \mu (E^y)$ is $\mathcal{B} $-measurable.