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0 $begingroup$ To study the convexity of this function I calculate the Hessian but is complicate to find is semi-definite positive or negative. real-analysis share | cite | improve this question asked Jan 15 at 20:39 Giulia B. Giulia B. 512 3 11 $endgroup$ $begingroup$ Let $g(x) = int_0^x e^{t^2} dt $ for $x ge 0$. It is convex and increasing. The function $(x,y) mapsto x^2+

0 $begingroup$ Let $I$ an interval on $mathbb{R}$ such as $I=(a,b)$ , with $a$ or $b$ could be equal to infinity. And we have $fin mathcal{L}^1(I,mathcal{B}(I), lambda)$ , then do we have always $$int_{(a,b)}fdlambda= int_a^bf(x)dx$$ and if not ! When we have this equality, knowing that $fin mathcal{L}^1(I,mathcal{B}(I), lambda)$ ? integration lebesgue-integral riemann-integration share | cite | improve this question edited Jan 15 at 20:42 Bernard 124k 7 41 118 asked Jan 15 at 20:39