[FOM] a question about L-measurable set

[Yu Liang]

Here R denotes the real set in V.

Is there a model of ZFC say M so that there is  a model of ZFC say M' \supset 
M  so that M' \models u(R  \cap M)>0 and M' \models u(R  \cap (M'\M))>0?

Is it possible  L=M?

Thanks

Liang Yu