  Double-differential three-jet production cross-sections are measured in
proton-proton collisions at a centre-of-mass energy of $\sqrt{s} = 7$ TeV using
the ATLAS detector at the Large Hadron Collider. The measurements are presented
as a function of the three-jet mass $(m_{jjj})$, in bins of the sum of the
absolute rapidity separations between the three leading jets $(|Y^\ast|)$.
Invariant masses extending up to 5 TeV are reached for $8< |Y^\ast| < 10$.
These measurements use a sample of data recorded using the ATLAS detector in
2011, which corresponds to an integrated luminosity of 4.51 fb$^{-1}$. Jets are
identified using the anti-$k_t$ algorithm with two different jet radius
parameters, R=0.4 and R=0.6. The dominant uncertainty in these measurements
comes from the jet energy scale. Next-to-leading-order QCD calculations
corrected to account for non-perturbative effects are compared to the
measurements. Good agreement is found between the data and the theoretical
predictions based on most of the available sets of parton distribution
functions, over the full kinematic range, covering almost seven orders of
magnitude in the measured cross-section values.
