Using the definition of measurable function show that any Co

Using the definition of measurable function show that any Constant function is measurable.

Solution

Answer :

Let (X;A) and (Y;B) be measurable spaces. A function f :XY is measurable if f^-1(B) A for ever BB.

Let h(x) = c . Let b R.

If b < c then h^-1( ( - , b ] ) = Ø F .

If b c then h^-1( ( - , b ] ) = X F . Thus h is measurable.