Posted by sxxx123456 on Saturday, January 17, 2009 at 12:39pm.
Let E(1,2) be the set of all numbers in (0,1) such that there decimal
representation does not contain 1 and 2. Prove that E(1,2) is lebesgue
measurable and find the lebesgue measure of E(1,2).
Would you please explain it step by step?

Needs math analysis teacher  Damon, Saturday, January 17, 2009 at 2:00pm
Not my thing :(

math  Count Iblis, Saturday, January 17, 2009 at 6:24pm
I would suggest you try to compute the lebesgue measure of E(1,2) first without being rigorous.
Use the principle of inclusion and exclusion to evaluate the probability that a randomly drawn number in the interval (0,1) does not contain a 1 or 2.
Then, use your computation to give a rigorous proof using the properties of the Lebesgue measure.
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