For 
,
there exist no additive finite and invariant measures for the group of displacements
in 
.
Hausdorff Paradox
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References
Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 49, 1983.Referenced on Wolfram|Alpha
Hausdorff ParadoxCite this as:
Weisstein, Eric W. "Hausdorff Paradox." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HausdorffParadox.html