Clarifying Integral Limits in Equation 4.6: A Scientific Analysis

[SP90]

http://arxiv.org/pdf/0807.1310v5.pdf

Equation 4.6 strikes me as wrong. The integral is \int_{0}^{\infty} B \mathrm{d}B

The limits of the integral seem to be values of z, but the integral seems to be wrt B. If the limits were values of B, the answer would be ∞. It's clearly not, but I don't understand this.

 

[mikeph]

It looks like he's canceled the dz from numerator and denominator in 4.5 and is left with BdB, but instead of writing the limits as B(z=0) and B(z=inf), they've just written 0 and inf.

The limits would be correct before dz were cancelled, but after, they should be changed. If this is the correct interpretation then I agree it's a little sloppy.