fly space
n.— «The board also recently decided to retain a storage area over the new auditorium, commonly known as a fly space, which was part of the original plan. For the last two months, the board discussed the need for the space commonly used for storage of sets and backdrops in stage productions.» —“Sparta Board of Education picks design for high school renovation” by Stephen J. Novak New Jersey Herald (Newton, New Jersey) May 23, 2007. (source: Double-Tongued Dictionary)
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The “fly space” is also commonly referred to as the “fly loft”.
When a set in a stage production is suspended from the ceiling and lowered into place, as opposed to being moved onstage from the wings, it is said to be ‘flown’.
This area of the theatre above the stage is known as the ‘loft’, hence, where sufficient room is made for flown sets, it becomes a ‘fly loft’.
The volume contained by the fly loft could easily be described as ‘fly space’