If $A$ is a null set and $B$ is a countable set, both in $\mathbb{R}$ can anyone help me show that $A+B$ is null.
So I'm slightly unsure of where to start here, but how about assuming that $A+B$ is not null. therefore there must exist an interval of real numbers in $A+B$, but that would be uncountable, contradiction. Am I along the right lines here?