Real Analysis Answers

Let 0 < a≤ b<1 show that there is no lebesgue measurable set A is subset of R such that aλ(I)≤λ(A∩I)≤bλ(I) for any open interval I subset of R

Let 0 < a≤ b<1 show that there is no lebesgue measurable sex A is subset of R such that aλ(I)≤λ(A∩I)≤bλ(I) for any open interval I subset of R

Let C is a subset of [0,1] be the cantor set and let f: [0,1]→[0,∞) be given by f(x)=0 on C and f(x)=n, in each complementary interval of length 3^(-n) show that f is lebesgue measurable and compute ∫_0^1▒〖f(x)〗dx

If A is lebesgue measurable subset of R of positive measure and 0< δ< X(A) .then show that there exists a measurable subset B of A satisfying λ(B)=δ

Find a bijection f:(a,b) --->(0,1)

prove that f(x) =x/(x squire+1),x is belongs to set of real number, is bijection.

S={n:n belongs to Z} what is the Sup S and Inf S? please explain the answer?

When a number set is not bounded above the supremum is plus infinity and when a set is not bounded below the infimum is minus infinity why?
please explain with examples

A number set has no supremum or it has a supremum which is infinity . does the two statement same ?

What is the domain of arcsin(Sin(x))?