I'm having a really hard time searching for the exact term to refer to quantifiers that are of NP+PP combinations. E.g.: a lot of, lots of, a bit of, plenty of, a number of, an amount of, etc. "Basic" quantifiers are single word quantifiers (e.g.: few, much, many, several, etc.), but what are the NP+PP combinations called? Are they quantifying expressions? They're not compund quantifiers, are they?
How are they analysed in phrase structure form? Let's take for example "a lot of sugar". Should the quantifier "a lot of" go under the node "Det", should the whole phrase be analysed as [[NP[Det+N]]+[PP[Prep+[NP[N]]]]], or is there an X-bar involved somewhere?