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Do sets with positive Legesgue Lebesgue measure have same cardinality as R? |
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I have been thinking about which kind of wild non-measurable functions you can define. This led me to the question: Is it possible to prove in ZFC, that if a (Edit: measurabel) set $A\subset \mathbb{R}$ has positive Lebesgue-measure, it has the same cardinality as $\mathbb{R}$? It is obvious if you assume CH, but can you prove it without CH? |
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Do sets with positive Legesgue measure have same cardinality as R?I have been thinking about which kind of wild non-measurable functions you can define. This led me to the question: Is it possible to prove in ZFC, that if a set $A\subset \mathbb{R}$ has positive Lebesgue-measure, it has the same cardinality as $\mathbb{R}$? It is obvious if you assume CH, but can you prove it without CH?
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