Additive function, locally bounded at zero
95340
Locally bounded additive function is linear
74876
Limit of Integral of Difference Quotients of Measurable/Bounded $f$ Being $0$ Implies $f$ is Constant
69695
$f\geq 0$, continuous and $\int_a^b f=0$ implies $f=0$ everywhere on $[a,b]$
16743
Graph of real continuous function has measure zero
158407
derivative bounded by a constant multiple of the function
51260
Sum of sets of measure zero
28315
Monotone functions and non-vanishing of derivative
76790
Condition to guarantee $f=0$ on $[a,b]$
66481
Convergence of characteristic functions to $1$ on a neighborhood of $0$ and weak convergence
119060
What can you say about a continuous function that is zero at all integer values?
139614
Polynomial bounded real part of an entire function
68617
Show that an entire function that is real only on the real axis has at most one zero, without the argument principle
145265
A non-zero function satisfying $g(x+y) = g(x)g(y)$ must be positive everywhere
6186
An Integrable function which is not essentially bounded on any subinterval of $[0,1]$
101776
Bounded solution for an equation
122519
Multiplicative Functions
74810
A function $f$ such that $f' = 0$ when $x < 0$ and $f' = 1$ when $x \geq 0$?