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It's both because it can be inside or a building or outside. WordPerfect even agrees with me.
In my opinion in (meaning inside) in italian you can transalate with CON, but THE FOCUS are "these premises". Of course most of the people choosed ON, but I'm a smoker, not heavy smoker, but I LIKE TO SMOKE and seeing the PRICES, I'd better use the preposition IN, Anyway, seeing that, for sure, it's a matter of MEDIA, Is Correct ON preposition.