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%2F00791040-5f5f-4ae8-8953-1e3f882cfc0f%2F3c6be8f9-0885-4e53-97e5-303e8282a53f%2Fqltm25_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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