(1)Is there a real-valued function f satisfies
the set {(x,f(x)),x belongs to R} is a second category subset of R2?
(2)Is there a real-valued function f satisfies
the set {(x,f(x)),x belongs to R} is non-measurable in the Lebesgue sense?
(1)Is there a real-valued function f satisfies
the set {(x,f(x)),x belongs to R} is a second category subset of R2?
(2)Is there a real-valued function f satisfies
the set {(x,f(x)),x belongs to R} is non-measurable in the Lebesgue sense?
Hint: For any non Lebesgue measurable, choose the indicator function
Hint: Use the Baire's Category Theorem: Every complete metric space is of second category.Is there a real-valued function f satisfies the set {(x,f(x)),x belongs to R} is a second category subset of R2?