Complex sentence: A point process needs to be defined on an underlying mathematical space, which in this article and often elsewhere is "d"-dimensional Euclidean space, denoted here by\\ textstyle\\ textbf ^, although point processes can be defined on more abstract mathematical spaces.
Split into simpler sentences: A point process needs to be defined on an underlying mathematical space. Often this space is "d"-dimensional Euclidean space denoted here by\\ textstyle\\ textbf ^, although point processes can be defined on more abstract mathematical spaces.