Complex sentence: These functions are always positive and are closely associated with Hilbert Spaces because they are frequently used to approximate distances between points and in a more general sense, encode a notion of distance within a space Bishop, 299.
Split into simpler sentences: These functions are always positive and are closely associated with Hilbert Spaces because their form is associated with distance metrics between points. In a more general sense, they can encode a notion of distance within a space Bishop, 299.