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stukbv
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Homework Statement
Take f: (a,b) --> R , continuous for all x0in (a,b)
and take (Ω = (a,b) , F = ( (a,b) [itex]\bigcap[/itex] B(R)) where B(R) is the borel sigma algebra
Then prove f is a borel function
The Attempt at a Solution
I know that continuity of f means that for all x in (a,b) and all ε>0 there exists a δ>0 such that |x-x0| < δ implies |f(x)-f(x0| < ε
And I want to show that {x in (a,b) s.t f(x) < c } is in F
But Then I am stuck, how would I use these facts to help me ?
Thanks in advance for any help