A Lorentzian Gromov Hausdorff notion of distance

This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov Hausdorff distance which makes this moduli space into a metric space. Further properties of this metric space are studied in the next two papers. The importance of the work is in fields such as cosmology, quantum gravity and—for the mathematicians—global Lorentzian geometry.