Siberia doesn't quite count though.. since it was empty. It's like claiming that the Antarctic is part of your Empire. Even if everyone agrees, it won't matter, because nobody lives there and it's not useful land in any way (at least not in any obvious way). It just serves to make the empire appear larger on a map.

Another funny thing about the Mongol Empire: because Kublai Khan lived in Beijing, the capital, many Chinese claim that the Mongolian Empire as their Empire. So, applying that logic elsewhere, does that mean that the Roman Empire suddenly became the Ravennan Empire when it changed its capital temporarily?