\frac{1}{|\partial B(x,r)|}\int_{\partial B(x,r)}u(y)\,dS(y)=\frac{1}{|\partial B(0,1)|}\int_{\partial B(0,1)} u(x+rz)\,dS(z)
Why does dS(y)\to dS(z) and not dS(y)\to dS(x+rz)?
If you want more information, it comes from http://www.stanford.edu/class/math220b/handouts/laplace.pdf on page 8...