# constructing Lebesgue measure

How would the construction of the Lebesgue measure in R2 change if we assume at the beginning that the measure of the unit square [0, 1]Ã?[0, 1] is =2? What would the measure of a circle of radius 1 be? Why?

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Well, if this is the only change we make in constructing Lebesgue measure, then the result will be a measure (not Lebesgue, of course) with all other properties preserved. The formal definition of _a_ measure only ...

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Advice for constructing Lebesgue measures is incorporated.

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