Is a real-analytic function which vanishes on a set of positive measure identically zero?
141254
Zeros of analytic function of several real variables
28315
Monotone functions and non-vanishing of derivative
21954
A question about $f(x)\equiv 0$
108846
Estimate of analytic function in a unit disk
68617
Show that an entire function that is real only on the real axis has at most one zero, without the argument principle
11322
Show that $f$ vanishes identically.
42942
Finding the number of analytic functions which vanish only on a given set.
113888
Behavior of derivative near the zero of a function.
136628
Measure theory convention that $\infty \cdot 0 = 0$
123249
An analytic function $f$ on $|z|<1$ with $\sup_{|z|<1} |f(z)|=1$ and $|f(0)|=\frac{1}{2}$ has no zeros in $|z|<\frac{1}{2}$
154621
A set with a finite integral of measure zero?
64797
Does an absolutely integrable function tend to $0$ as its argument tends to infinity?
98717
Are all measure zero sets measurable?
53848
$f$ holomorphic on $D\setminus \{0\}$ and takes no values in $(-\infty,0],$ then $0$ removable
110395
Integrable function $f$ on $\mathbb R$ does not imply that limit $f(x)$ is zero
148474
on the boundary of analytic functions
59745
Behavior of holomorphic functions on the boundary of the unit disk