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?
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?
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F76ddde16-ec7d-4ab3-a988-b2e6307ba87c%2F8e80b637-7276-4a0f-a10f-c4da28e75763%2Fkep7uk_processed.jpeg&w=3840&q=75)
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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