Read this: In a series of famous papers, von Neumann made spectacular contributions to measure theory. The work of Banach had implied that the problem of measure has a positive solution if n = 1 or n = 2 and a negative solution in all other cases. Von Neumann's work argued that the "problem is essentially group-theoretic in character, and that, in particular, for the solvability of the problem of measure the ordinary algebraic concept of solvability of a group is relevant. Thus, according to von Neumann, it is the change of group that makes a difference, not the change of space."
Now answer this question, if there is an answer (If it cannot be answered, return "unanswerable"): What concept was relevant to the solvability of the problem of measure?
algebraic concept of solvability of a group is relevant