Why is ω(f;[-a,a];δ) = ω(f;[0,a];ε) for an even function?

[matt_747]

If f is an even function on [-a,a] , show that ω(f;[-a,a];δ) = ω(f;[0,a];ε) .

help will be appreciated so much

 

[rochfor1]

Could you explain your notation? It's not entirely standard.

 

[matt_747]

ω(f;[a,b];δ)= sup |f(x)-f(y)| that x,y ϵ[a,b] and |x-y|≤δ