We define a translation-invariant measure and integral on GL₂ over a two-dimensional local field F by combining elements of the classical GL₂ theory and the theory developed by Fesenko for the field F itself. We give several alternate expressions for the integral, including one which agrees with the integral defined previously by Morrow.

This work was completed while the author was supported by an EPSRC Doctoral Training Grant at the University of Nottingham.