1. 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. (a) Prove that X is Lebesgue measurable. (b) What is the Lebesgue measure of X?
1. 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. (a) Prove that X is Lebesgue measurable. (b) What is the Lebesgue measure of X?
Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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![1. 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.
(a) Prove that X is Lebesgue measurable.
(b) What is the Lebesgue measure of X?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c1f89a6-8b63-43d7-8621-7e30688f79c7%2F0b3c6557-b05f-43d5-b248-13164b224788%2Fqnvu66a_processed.png&w=3840&q=75)
Transcribed Image Text:1. 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.
(a) Prove that X is Lebesgue measurable.
(b) What is the Lebesgue measure of X?
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