Due date: November 24 Problem 1 If the measurable $latex f_n\searrow f\ge 0$ with $latex \int f_1 < \infty$, then $latex \int f_n \to \int f.$ Explain the condition $latex \int f_1 < \infty$. Problem 2 Let $latex f\in L^1(\R)$ and $latex f^\delta(x) = f(\delta x)$. Then $latex \displaystyle \int f^\delta = \frac{1}{\delta}\int f.$ Problem 3 There exists a positive continuous $latex f \in L^1(\R)$ such that $latex \limsup_{|x|\to\infty} f(x) = \infty.$ If $latex f\in L^1(\R)$ is uniformly continuous, then $latex \lim_{|x|\to\infty}f(x) = 0.$ Problem 4 If $latex f\in L^1(\R)$ and $latex F(x) = \int_{-\infty}^x f$. Then F is uniformly continuous.