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Total $γ^{\star}γ^{\star}$ cross section and the BFKL pomeron

In the framework of the dipole picture of the BFKL pomeron we discuss a few possibilities of calculating the total $γ^{\star}γ^{\star}$ cross section of the virtual photons. We argue that the existing successful fits of the dipole picture formulae to the measured structure functions $F_2(Q^2,x)$ favor one of the possible extensions of the dipole picture of the BFKL pomeron formulated recently by one of us.