Ah, there's some interesting history on this compilation.
Aladdin, wasn't even originally part of Arabian Nights (or 1001 Nights, the names are not joined). He, along with some other famous stories were later added by a translator named Antoine Galland.
Aladdin's name is arabic. But, the original story is set in a Chinese city. His character is described as being explicitly chinese, even though the China in that tale is an Islamic culture and the characters all have Arabian names.
So, it makes you wonder if China was written in as a cultural mistake.
Wikipedia has more on Aladdin's history.
Also check out, the back story on 1001 Nights.