(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that the characteristic function [itex]\chi_A: X\rightarrow R, \chi_A(x)=1,x\in A; \chi_A(x)=0, x\notin A[/itex], where A is a measurable set of the measurable space [itex] (X,\psi) [/itex], is measurable.

2. Relevant equations

a function [itex]f: X->R[/itex] is measurable if for any usual measurable set M of R, [itex]f^{-1}(M)[/itex] is measurable in [itex](X,\psi)[/itex]

3. The attempt at a solution

Obviously [itex]f^{-1}([0,1])=X[/itex], where the universal set X need not be a measurable set in a general measurable space [itex](X,\psi)[/itex], which only requires that the (uncountable) union of all measurable sets is X. But the book explicitly asked to prove for a general measurable space. What am I missing here? Thank you.

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# Homework Help: Simple question about measurable characteristic function

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