Hi,
I have lemma to prof about asymptotic equal functions, could you please advise me on it?
Let [MATH]h_{i}:R^{2}→R[/MATH] for [MATH]i=1,2[/MATH] such that [MATH]h_{1}(x,y)\underset{x→a}{\asymp} h_{2}(x,y)[/MATH] for all [MATH]y∈R[/MATH], and integrals [MATH]\int_{-\infty}^{+\infty}h_{i}(x,y)dy[/MATH] exists. Then:
[MATH]\int_{-\infty}^{+\infty} h_{1}(x,y)dy \underset{x→a}{\asymp}\int_{-\infty}^{+\infty} h_{2}(x,y)dy[/MATH]
Any ideas?
I have lemma to prof about asymptotic equal functions, could you please advise me on it?
Let [MATH]h_{i}:R^{2}→R[/MATH] for [MATH]i=1,2[/MATH] such that [MATH]h_{1}(x,y)\underset{x→a}{\asymp} h_{2}(x,y)[/MATH] for all [MATH]y∈R[/MATH], and integrals [MATH]\int_{-\infty}^{+\infty}h_{i}(x,y)dy[/MATH] exists. Then:
[MATH]\int_{-\infty}^{+\infty} h_{1}(x,y)dy \underset{x→a}{\asymp}\int_{-\infty}^{+\infty} h_{2}(x,y)dy[/MATH]
Any ideas?