Large upper-level floor spaces directly below the roof of commercial buildings or warehouses, originally unpartitioned but often modified for secondary use; may also be used for domestic sleeping or storage platforms set close to ceilings or roofs and open to and overlooking a living space below. For enclosed spaces under sloping roofs, between the roof and the ceiling of the uppermost story, especially in houses, use "attics (interior spaces)." For substantial interior spaces at the level of an upper story, usually extending the full length or width of rooms, use "galleries (upper level spaces)."

Source: AAT

http://vocab.getty.edu/page/aat/300255116