Prove that there exists a continuous function $g$ such that $\int_a^b|f-g| \lt \epsilon$
48246
Approximation of Riemann integrable function with a continuous function
113740
Find a uniformly continuous function such that $a_{n+1}=f(a_n)$
64619
Continuity of a function of product spaces
9320
Extension of continuous function on a closed subset of $\mathbb{R}$
150554
proof that $f'$ is continuous at $a$
11828
continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
53627
Proving continuity of $f$
94971
For every $\epsilon>0$ there exists $\delta>0$ such that $\int_A|f(x)|\mu(dx) < \epsilon$ whenever $\mu(A) < \delta$
134752
Proof (epsilon delta) for the continuity of a function at a point
44269
If $f$ is nonnegative and continuous on $[a,b]$, then $\left(\int_a^b f(x)^n \ dx\right)^{1/n}\to\max\limits_{[a,b]} f$
42853
If $f \geq 0$ is continuous and $\int_{a}^{b} f(x) \, dx = 0$, then $f =0$
118207
Prove that the product of two continuous functions is continuous
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
69656
Prove or disprove that $\int_a^b |f(x)|\ \mathrm{d}x\geq \big | \int_a^b f(x)\ \mathrm{d}x\big| $
4062
prove that $f(x)=\log(1+x^2)$ is Uniform continuous with $\epsilon ,\delta$ ...
63836
Show there exists $g:(0,1)\to\mathbb{R}^2$ such that $h\circ g$ constant, $g$ continuously differentiable and $g$ injective
105769
Prove that $\exists a, b\in(0,1)$ such that $\int_0^{a} xf(x)dx=0\text{ and }\int_0^bxf(x)dx=\frac{b^2f(b)}{2}.$