Deep-inelastic events containing a measured jet as a probe of QCD behavior at smallx

We examine the proposal that deep-inelastic ($x,Q^2$) scattering events which contain an identified jet, with transverse momentum squared $k^2\simeq Q^2$, allow an ideal determination of the QCD behavior at very small $x$. We solve the Lipatov equation to predict the shape of the jet spectrum in such events and show that measurements at the DESY $\mathrm{ep}$ collider HERA should be able to verify, inter alia, whether the gluon indeed has the theoretically anticipated $g\sim x^{{-\alpha }_P}$ small-$x$ behavior with the intercept ${\alpha }_P$ of the bare perturbative QCD Pomeron possibly as large as 1.5.