The BORE is measured 9" from the breech. The barrel walls are measured over every inch of the barrel.

There is no legal minimum thickness for barrel walls. If a gun with 12 thou barrels is submitted for proof and it survives the proof load, it will be stamped with the requisite proof marks.

Usually, the barrels are at their thinnest 4-8 inches from the muzzles.

A number of factors affect the viability of a gun with thin barrels:
Is it in proof? - For this, you need to measure the bore.

Is it pitted or bulged or dented or otherwise defective?

What is the profile of the whole barrel? I recently worked on an old Purdey with 20 thou plus everywhere except a gradually tapered 3" section, 6" from the muzzles, where it went down to 17 thou.

The gradual taper imparts less stress than a steep change of profile. The gun had otherwise clean 30" barrels with True Cylinder and Half Choke.

The gun was in proof and in otherwise good condition and very reasonably priced. It constituted a viable shooter if used with 65mm cases and 1oz loads and used with care. As aprevius poster said - the key thing is to avoid getting any dents in it.

Greener once carri3d out experiments where he reduced the last third of the barrel walls until he could cut them off wuith a penknife. With each reduction in thickness, he fired the gun. At no point did the walls fail upon firing.