$\forall \epsilon >0, \exists \sigma >0$ such as : $ [\forall A\in F : P(A)<\sigma ]\Rightarrow [\int_A |x| dP $
94971
For every $\epsilon>0$ there exists $\delta>0$ such that $\int_A|f(x)|\mu(dx) < \epsilon$ whenever $\mu(A) < \delta$
31741
Show for $f:A \to Y$ uniformly continuous exists a unique extension to $\overline{A}$, which is uniformly continuous
12349
a construction of a continuous function from a normal space to [0,1]
155311
How to get a set $E$ such that $0<\mu(E\cap I)<\mu(E)$ for all interval $I$?
47419
Asymptotics of uniformly continuous functions over $\mathbb R$
98662
$P(|X|\ge\lambda a)\ge (1-\lambda)^2a^2$ for $0\le \lambda \le 1$
132747
How can one show that $ f(0)\ln(\frac{b}{a})=\lim_{\epsilon\rightarrow 0}\int_{\epsilon a}^{\epsilon b} \frac{f(x)}{x}dx$?
42842
Proof for $\epsilon$ closeness to $\sqrt{2}$ for all values of $\epsilon$
62118
Prove $\epsilon$-$\delta$ definition of continuity implies the open set definition for real function
45602
Show that is $\int_A f$ exists, then so does $\int_A |f|$
130998
Is $\exists x \in A ~:~ P(x)$ the same as $\exists x ~:~ x \in A \implies P(x)$
5251
If $F$ is closed, does there exist a finite measure on $[0,1]$ with support $F$?
74876
Limit of Integral of Difference Quotients of Measurable/Bounded $f$ Being $0$ Implies $f$ is Constant
115219
If $E$ is Lebesgue measurable, show that there exists a closed set $F$ with $F \subset E$ and $m(E\setminus F)<\epsilon$
113740
Find a uniformly continuous function such that $a_{n+1}=f(a_n)$
19072
$\int_{\mathbb R} |f(x)| dx < \infty \implies \int^{\infty}_{n} |f(x)| dx \to 0$ as $n \to \infty$?
132532
Things around $(\forall x)(\Psi \Rightarrow \Phi) \Leftrightarrow ((\exists z)\Psi) \Rightarrow \Phi)$