For periodic $f,g$ (and continuous), does $\lim (f-g) = 0 $ imply $f=g$?
64134
The difference between two periodic functions converges to zero, is this two functions identical?
9614
How does the existence of a limit imply that a function is uniformly continuous
42334
Does $\lambda$ $\mathbf u$ $= 0$ imply $\lambda = 0$ or $\mathbf u$ $= 0$?
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
35547
Does $\{f_ng_n\}\to fg$ uniformly?
89421
Does $\int_{1}^{\infty} g(x)\ dx$ imply $\lim\limits_{x\to \infty}g(x)=0$?
31319
An integrable and periodic function $f(x)$ satisfies $\int_{0}^{T}f(x)dx=\int_{a}^{a+T}f(x)dx$.
104510
For continuous $f$, $\int_0^x f(t)dt = ∫_x^1f(t)dt$ implies $f=0$.
25467
Prove that $\lim f(x) =0$ and $\lim (f(2x)-f(x))/x =0$ imply $\lim f(x)/x =0$
72847
Does $f(x)$ is continuous and $f = 0$ a.e. imply $f=0$ everywhere?
47026
if $f^{(n)}(x_0),g^{(n)}(x_0)$ exist and $\lim_{x\to x_0} \dfrac{f(x)-g(x)}{(x-x_0)^n}=0$ then $f^{(r)}(x_0)=g^{(r)}(x_0 )$ for all $0\leq r\leq n.$
35754
Is $f(x)=\sin(x^2)$ periodic?
132113
Does $f(x) = f(2x)$ for all real $x$, imply that $f(x)$ is a constant function?
31503
Question about Maximum Modulus Principle applied to $|f|+|g|$
29180
If $f(x/n)\to0$ when $n\to\infty$, for every $x$ and $f$ is continuous, then $f(x)\to0$ when $x\to0$, or not?
69695
$f\geq 0$, continuous and $\int_a^b f=0$ implies $f=0$ everywhere on $[a,b]$
92089
If $f:[a,b]\to \mathbb{R}$ is continuous and nonnegative and $\int_a^b{f}=0$, then $f(x)=0$ for all $x\in [a,b]$