Let $C$ be the Cantor set and $\mu$ be the uniform measure. Find $\int x^2 d\mu$
124462
Calculate integral with cantor measure
30694
Show that there exist $[a,b]\subset [0,1]$, such that $\int_{a}^{b}f(x)dx$ = $\int_{a}^{b}g(x)dx$ = $\frac{1}{2}$
140901
Uniform convergence of $f_n(z)=nz^n$ in the set $|z|<\frac{1}{2}$
95947
Cantor set + Cantor set =$[0,2]$
83873
Find $E(|X-Y|^a)$ where $X$ and $Y$ are independent uniform on $(0,1)$
41100
Density of sum of two independent uniform random variables on $[0,1]$
45205
Showing that $\int_0^\infty x^{-x} \mathrm{d}x \leq 2$.
84359
On Lebesgue Outer Measure of an interval
123197
$C^2 $embedded in holder space?
82361
How do you prove that $p(n \xi)$ for $\xi$ irrational and $p$ a polynomial is uniformly distributed modulo 1?
86115
Generating uniform points inside an $m$-dimensional ball
120599
Points of a Measure Zero Sets Covered by Intervals Infinitely Many Times
15586
Volume of the torus with an integral
130858
How can one find $\mu$?
69273
Is there a compact subset of the irrationals with positive Lebesgue measure?
51260
Sum of sets of measure zero
95260
Let $m$ be Lebesgue measure and $a \in R$. Suppose that $f : R \to R$ is integrable, and $\int_a^xf(y) \, dy = 0$ for all $x$. Then $f = 0$ a.e.