TITLE: Are all models of ZF + DC + "All set of reals are lebesgue measurable" also models of CH?
QUESTION [5 upvotes]: Possible Duplicate:
Lebesgue Measurability and Weak CH 

I have studied a little set theory and I found that Solovay constructed a model of ZF+DC+"All set of reals are Lebesgue measurable" and I found that the same model satisfies the "perfect set property" which implies that every uncountable subset of $\mathbb{R}$ is bijectable with $\mathbb{R}$. In other words, the Continuum Hypothesis (CH) is true in that model. I also found that the Axiom of Determinacy (AD) implies that every set of reals is Lebesgue measurable and it also implies the perfect set property.
Therefore, I have a question: Does ZF+DC+"All set of reals are Lebesgue measurable" always imply CH?

REPLY [5 votes]: The question seems to be an open research problem; it was posed in 2011 on MO (and has remained unanswered), see: 
Lebesgue Measurability and Weak CH