None of the fight scene itself...

was filmed at the Collaseum (I'm mis-spelling that, aren't I?) from what I've read. Can anyone clarify this? I remember someone (Bruce's cinematographer or camerman, maybe?) saying they had to rush to get the establishing shots there, they didn't have the permission to film there, so they didn't have time to film any of the actual fighting in Rome. I think Chuck has always said they shot the fight scene there because it makes a better story ("fighting" in the same place ancient gladiators had, that sort of thing).