distorted in redshift space because of the nonlinear relation between the redshift and the comoving distance, and of the nonlinear relation between the apparent angular size and the angular diameter distance. Suppose that there is a spherical object of diameter $l$ in units of comoving length. The redshift difference of this object is $\Delta z =
H(z) l/c$, and the apparent angular size is $\Delta\theta = l/D_{\rm
A}(z)$, where $H(z)$ is the redshift-dependent Hubble parameter and $D_{\rm A}(z)$ is the comoving angular diameter distance \[proper angular diameter distance is given by $d_{\rm A}(z) = D_{\rm
A}(z)/(1+z)$\]. The ratio $$\frac{\Delta z}{z\Delta\theta} = \frac{D_{\rm A}(z)}{cz/H(z)}
\label{eq2-11}$$ is unity for sufficiently small $z$. In deep redshift regions, however, the ratio significantly deviates from unity and the deviation pattern strongly depends on the density parameter ${{\mit \Omega}}_{\rm M0}$ and on the cosmological constant ${{\mit \Omega}}_{\Lambda 0}$, or parameters of the dark energy.

The redshift-space distortions of the two kinds, i.e., the velocity distortions and the AP distortions, are interwoven in the real universe except for the shallow redshift surveys without the AP effect. @bal96 derived the AP effect on the linear power spectrum, and @mat96 derived the same effect on the linear two-point correlation 