Does "Every set of $\mathbb{R}$ is Lebesgue measurable" imply some weakened LEM?

120 Views Asked by At

I would like to know if the Reverse Mathematics has a conclusion for this axiom ($\text{LM}$:Every set of $\mathbb{R}$ is Lebesgue measurable).

I have tried to translate this axiom into a halting problem like $\text{LPO}$, but without success.