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Function of real measurable functions is measurable

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Theorem
MeasureTheory

Let (X,M)(X,\mathscr{M}) be a measure space and let u,v:XRu,v:X\to \mathbb{R} be two measurable functions where R\mathbb{R} is equipped with the Standard topology. Suppose that (Y,T)(Y,\mathscr{T}) is a Topological Space and Φ:R2Y\Phi:\mathbb{R}^2\to Y is Continuous (here R2\mathbb{R}^{2} is also equipped with standard topology) then h:XYh:X\to Y defined as h(x)=Φ(u(x),v(x))h(x)=\Phi(u(x),v(x)) is measurable.

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