Please give a Lebesgue measurable subset E of Rn

and a Lebesgue measurable and finite-valued function f on E

satisfies

there doesn't exist a sequence of Lebesgue measurable subsets {Ek}k=1,2,...

of E

such that

(1)the untion of Ek is E;

(2)the restriction of f to every set Ek is continuous on Ek.