# Does measurability of cardinal $\kappa$ imply measurability of $2^\kappa$?

A cardinal $$\kappa$$ is real-valued measurable if there is a $$\kappa$$-additive probability measure on $$2^\kappa$$ which vanishes on singletons. The existence of measurable $$\kappa$$ is independent of ZFC.

Question: if $$\kappa$$ is assumed to be real-valued measurable, does it necessarily follow that $$2^\kappa$$ is real-valued measurable?