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The most thorough study of the $\ttbar$ threshold measurements was done in the context of the TESLA project in Ref.~\cite{Martinez_Miquel_2003}, the parameters of which are very close to those of the ILC. The study makes use of a multi-parameter fit of $m_{\rm top}$, $\Gamma_{\rm top}$, $\lambda_{\rm top}$ and $\alpha_{\rm s}$ to the top cross section, the top momentum distributions, and the forward-backward asymmetry. When constraining the value of $\alpha_s(m_{\rm Z})$ to its currently measured value, the study obtained statistical uncertainties of $\Delta m_{\rm top} = 31$~MeV/$c^2$, $\Delta\Gamma_{\rm top} = 34$~MeV, and a relative uncertainty on the Yukawa coupling $\lambda_{\rm top}$ of the order of $\pm 40\%$. The dominant experimental systematic uncertainties on the mass stem from the knowledge of $\alpha_s(m_{\rm Z})$ ($\pm 30$ MeV/$c^2$ per unit of $\pm 0.0007$, the current uncertainty on this quantity), and from the knowledge of the luminosity beam-energy  spectrum: a $\pm 20$\% uncertainty of the RMS width of the main luminosity peak would result in top mass uncertainties of approximately $\pm 75$ MeV/$c^2$, far in excess of the statistical uncertainty~\cite{cite:1303.3758}. The expected TLEP statistical uncertainties are summarized in Table~\ref{tab:TopMass}. In addition to the ten-fold increase in the number of $\ttbar$ events at TLEP, which reduces the statistical uncertainties by a factor of three, the much better knowledge of the beam-energy spectrum, and the precise measurement of the strong coupling constant with TeraZ and OkuW are bound to reduce the main experimental systematic uncertainties by one order of magnitude, hence below the statistical uncertainties. The starting design study plans to demonstrate fully the TLEP potential in this respect. A specific effort to reduce the theoretical Electroweak uncertainties on the cross section by one order of magnitude will also be needed.