Typical applications of Fubini's theorem and Radon-Nikodym Can someone please share references (websites or books) where I can find problems related with Fubini's theorem and applications of Radon-Nikodym theorem? I have googled yes and don't find many problems. What are the "typical" problems (if there are any) related with these topics? [Yes, exam is coming soon so I don't know what to expect and don't have access to midterms from previous years].
Thank you

One basic example of what you can do with Fubini's theorem is to represent an integral of a function of a function in terms of its distribution function. For instance, there is the formula (for reasonable $\phi$, $f$ basically arbitrary but nonnegative)
$$ \int \phi \circ f d\mu = \int_t \mu(\{ f> t\}) \phi'(t) dt$$ which reduces questions about integrals of, for instance, $p$th powers to questions about the distribution function. This is (for example) how the boundedness of the Hardy-Littlewood maximal operator  on $L^p$ ($p>1$) is proved: you get a bound on the distribution function of the maximal function by general methods and then do an interpolation process. 
To prove the formula above, as in Rudin, one can consider the collection $E$ of pairs $(x,t)$ such that $0 \leq t \leq f(x)$. This is a measurable subset of $X \times \mathbb{R}$ if $X$ is the initial measure space on which $f$ is defined and $\mathbb{R}$ has Lebesgue measure. 
Then, one can write the second integral in the displayed equation 
as $\int_t \phi'(t) dt \int_{x \in X} \chi_E(x,t) d \mu$ where $\chi_E$ denotes the characteristic function.
Now rearranging this integral via Fubini's theorem allows one to integrate with respect to $t$ first, for each $x$; then $t$ goes from $0$ to $f(x)$, and one can see that this integral becomes $\int_x \int_{t=0}^{f(x)} \phi'(t) dt$, which is the right-hand-side of the displayed equation.
