the distribution of magnifications $p(\mu)$ among all lensing events is given by $$p(\mu) = \frac{1}{\sigma}\int d^2{\mathbf{y}}\ \delta(\mu({\mathbf{y}})-\mu)$$ where $\sigma$ is the (unbiased) lensing cross section defined in Eq. \[eq:cs\], then we can rewrite Eq. \[eq:bcs\] as $$\sigma_B = {\left\langle \mu^{\alpha-1} \right\rangle}\sigma,$$ where $${\left\langle \mu^{\alpha-1} \right\rangle} = \int d\mu\ p(\mu)\mu^{\alpha-1}.$$ Thus, the net effect of gravitational magnification on the frequency of lensing events can be summarized as a biasing factor ${\left\langle \mu^{\alpha-1} \right\rangle}$ that multiplies the unbiased lensing cross section $\sigma$.**

Triaxiality and Lensing Biasing
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Let ${\mathbf{P}}$ characterize the mass distribution of a triaxial halo, and let ${\mathbf{\hat n}}$ be the orientation of the halo’s long axis relative to the line of sight. The halo’s two dimensional potential is then characterized by a new set of parameters ${\mathbf{p}}({\mathbf{P}},{\mathbf{\hat n}})$ which depend on the halo properties ${\mathbf{P}}$ and the particular line of sight ${{\mathbf{\hat n}}}$ along which the halo is being viewed. For instance, the vector ${\mathbf{P}}$ can include such halo properties as halo mass and axis ratios, whereas ${\mathbf{p}}$ could include parameters such as the Einstein radius of the projected mass distribution as well as the projected axis ratio.

As discussed above, the mean number of lensing events per unit 