BoundedRegionQ
BoundedRegionQ[reg] gives True if reg is a bounded region and False otherwise.
Examples
Test if region is bounded:
BoundedRegionQ[Disk[]]
(* True *)Unbounded region:
BoundedRegionQ[HalfPlane[{0, 0}, {1, 0}]]
(* False *)Please visit the official Wolfram Language Reference for more details.