correlation function $\xi_{\rm obs}$ in a given redshift interval ${\cal Z}$ is $$\xi_{\rm obs}(r) = { \int_{\cal Z}   
d z_1 d z_2 {\overline{\cal N}}(z_1) {\overline{\cal N}}(z_2)   
~b_{\rm eff}(z_1) b_{\rm eff}(z_2)   
\xi_{\rm m}(r,\bar{z})   
\over \bigl[ \int_{\cal Z} d z_1   
{\overline{\cal   
N}}(z_1) \bigr]^2 } \;,   
\label{eq:xifund}$$ where ${\overline{\cal N}}(z)\equiv {\cal N}(z)/r(z)$, ${\cal N}(z)$ is the actual redshift distribution of the catalog and $r(z)$ describes the relation between comoving radial coordinate and redshift. Here $\bar{z}$ is a suitably defined intermediate redshift. The method has been extended to include the effects of redshift-space distortions using linear theory and the distant-observer approximation [@kaiser].

A fundamental role in the previous equation is played by the effective bias $b_{\rm eff}$. In fact the final aim of models dealing with clustering is to determine the behavior of the bias factor, once a given theoretical picture is assumed. In practice the effective bias can be expressed as a weighted average of the ‘monochromatic’ bias factor $b(M,z)$ of objects with some given intrinsic property $M$ (like mass, luminosity, etc): $$b_{\rm eff}(z) \equiv {\cal N}(z)^{-1} \int_{\cal M} d\ln M' ~b(M',z)   
~{\cal N}(z,M')\, ,   
\label{eq:b_eff}$$ where ${\cal N}(z,M)$ is the number of objects actually present in the catalog with redshift within $dz$ 