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Let F be a family of subsets of a set X such that empty set is the element of F. A subset A of X belongs to F1 if and only if either A is a subset of F or complement of A is the subset of F. A subset B of X belongs to F2 if and only if B is a finite inter...

Let S be the set of all measurable functions on [0,1]. Then the set O of all functions in S equal to 0 a.e on [0,1] makes an additive subgroup of a commutative group S. Show that S/O with the distance p(f,g)=indefinite integral(0,1)((|f(x)-g(x)|)/(1+|f(x)...

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?

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).

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?

becouse they couldn't help me :(

thank you but what will ý do at the end?