Let X be the set of all real numbers in [0, 1] whose infinite decimal expansion does not contain a 2 or a 7. For example, 1/3 = 0.333... EX, while 7/5 = 0.628... X. Prove that X is Lebesgue measurable. What is the Lebesgue measure of X?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
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Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 62E
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Let X be the set of all real numbers in [0, 1] whose infinite decimal
expansion does not contain a 2 or a 7. For example, 1/3 = 0.333... € X,
while 7/5 = 0.628... X.
Prove that X is Lebesgue measurable.
What is the Lebesgue measure of X?
Transcribed Image Text:Let X be the set of all real numbers in [0, 1] whose infinite decimal expansion does not contain a 2 or a 7. For example, 1/3 = 0.333... € X, while 7/5 = 0.628... X. Prove that X is Lebesgue measurable. What is the Lebesgue measure of X?
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