Let's say I have a Lebesgue integrable function $f: X \to \mathbb{R}$, where $X$ is an arbitrary measure space. Now, suppose I want to find the measure of the set $$ A = \{x \in X: f(x) \geq c\} $$ for some $c \in \mathbb{R}$. Is there a way that I can express $\mu(A)$ in terms of $\int f$? Note that $A$ is measurable by definition of a measurable function. I'm not looking for a fancy way to do this; I'm new to this topic and I'm wondering whether there is an easy expression.
Edit 1: If not an exact relationship, is there an inequality?
Following Cameron Williams, an inequality is given by $\mu(\{f\geq c\})= \int_ {\{f\geq c\}} 1\, d \mu \leq \frac{1}{c} \int f d\mu,$ since $\frac{f}{c} \geq 1$ on $\{f\geq c\}$.