Recent content by rustyjoker

Homework Statement Prove (using Lebesgue outer measure) that $$m_{2}^{*}(\{(x,y)\in\mathbb{R}^{2}\colon x>1,0<y<x^{-2}\})=m_{2}^{*}(A)<\infty$$ The Attempt at a Solution I'm not sure if this is valid proof but I'd have done it like this: $$\int_{1}^{k}\left|x^{-2}\right|\, dx <\infty \forall...

you can't take logarithm because you can't know if 1-sum(x_i)^2 is negative or not.

Homework Statement I need to prove that (1+x_{1})·...·(1+x_{n})≥(1-Ʃ^{n}_{i=1}x_{i}^2)e^{Ʃ^{n}_{i=1}x_{i}} with all 0≤x_{i}≤1 I've already proven that (1+x_{1})·...·(1+x_{n})≤e^{Ʃ^{n}_{i=1}x_{i}} with all 0≤x_{i}≤1 and (1-x_{1})·...·(1-x_{i})≥1-Ʃ^{n}_{i=1}x_{i} with all 0≤x_{i}≤1 , but...

Well, for an example if you think about the product (1+0,009)(1+0,008)⋅...⋅(1+0,001)=1,045879514 and exp(0,009+...+0,001)=1,046... I think the idea is to proof that first lim_{k→}∞ n_{k}=∞, then lim_{k→}∞ x_{k1}=...=lim_{k→}∞ x_{k_{nk}}=x/n_{k}= 0. So we'd have lim_{k→∞}...

Homework Statement Big problem with exponential function proof assignment, need some help. let x≥0 and for every k\in N there is n_{k}\in N and x_{k1}≥...≥x_{k_{nk}} and x_{k1}+...+x_{k_{nk}}=x. Proof: if lim_{k→}∞ x_{k1}=0 then lim_{k→}∞ (1+x_{k1})·...·(1+x_{k_{nk}})=exp(x)=e^{x}