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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