Let X=[0,1],λ be the Lebesgue measure on [0,1] and L(X) be the set of Lebesgue sets measurable on [0,1]. The triplet (X,L(x),λ) is the Lebesgue space on [0,1]. Calculate the Lebesgue measure of the following sets; a) {1/2} b) (1/2,1] c) [0,1/2)
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Let X=[0,1],λ be the Lebesgue measure on [0,1] and L(X) be the set of Lebesgue sets measurable on [0,1]. The triplet (X,L(x),λ) is the Lebesgue space on [0,1]. Calculate the Lebesgue measure of the following sets;
a) {1/2}
b) (1/2,1]
c) [0,1/2)
Please be as clear as possible, legible, and explicative in all the steps. Use definitions if necessary. Thank you very much
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