Just read the last two lines of pg2 of the notes http://www.cims.nyu.edu/~chou/notes/harmonic, why the last integral is supported on $\{|f(x)| > \alpha\}$ but not $\{|f(x)|\geq\alpha\}$? Since we can define $f(x,\alpha)=1.\alpha^{p-1}$ which is supported on the set $\{(x,\alpha)\in (R^n,R)|0\leq\alpha\leq f(x)\}$ , fubini theorem should come in here .
Can anyone give me a more detailed explanation of the proof by using fubini ? Thanks in advance .