The term "over" is commonly used in mathematical exposition as a synonym for "in the domain of." So, for example, "Let be a function over the reals" means "Let be a function defined for ."
Over
See also
Domain, ElementExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Over." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Over.html