there being a lot of...
先说imagine后接动名词作宾语
imagine doing sth
imagine sb's doing sth
imagine sb doing sth
原来的句子：
imagine there is a lot of fun about it
这里的there在本结构中被当作了句子主语的.
所以,改成复合结构时就是there being
又如：
You can imagine there being a lot of fuss about it.
你可以想象人们对这件事情大惊小怪.
None would dream of there being such a place.
——of的后头本来要接的是“there was such a place.”但介词后不接that从句的.