Let X be a compact Haussdorff topological group and let m be the Haar measure on X. Can we find a meager set in X whose complement is m-null? I can do it when X is separable but I don't know if there could be a non separable counterexample. The only non separable examples I know are products of separable groups so this holds there.

Thanks for your help!

Let X be a compact Hausdorff topological group and let m be the Haar measure on X. Can we find a meager set in X whose complement is m-null? I can do it when X is separable but I don't know if there could be a non separable counterexample. The only non separable examples I know are products of separable groups so this holds there.

Thanks for your help!