The normal vector of this line (drawn in red) can be interpreted as the P dimension
How does one define the normal here? In general, we don't have any inner product in our framework, do we? A vector measure generally takes values in a Banach space, not a Hilbert space... For representing preferences, do we have to have a Hilbert space instead? I have a similar question about the later line:
This allows us to define a preference relation E1≥E2 based on the angle of E1 being within 180° of E2's
How does one define the normal here? In general, we don't have any inner product in our framework, do we? A vector measure generally takes values in a Banach space, not a Hilbert space... For representing preferences, do we have to have a Hilbert space instead? I have a similar question about the later line: