Dense sequences

Give a example of countable subset l^2 ( it is the class of all sequences which are bounded ) which is dense in l^2 ?

Open and closed set

Show that every open subset of metric space is the union of countably many closed sets?

Lebesgue measurable sets in R^n

Prove that Lebesgue measurable sets in R^n form a sigma-algebra in R^n.

Q on Lebesgue measures

M*(A) = inf ( A subset of M) of the sum of |M_i|. If A is a subset of K_s, where K_s = { -s =< x_i =< s} Then show that M*(A) = S^n - M*(A^c) A^c is compliment of A ( I think compliment of A in K_s ? )

Description of the working of the Jacobians with Trigonometric Functions.

Real Analysis Jacobians (XXII) Description of the working of the Jacobians with Trigonometric Functions.