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?© BrainMass Inc. brainmass.com December 15, 2020, 6:17 pm ad1c9bdddf
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 ...
Advice for constructing Lebesgue measures is incorporated.