ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation F6614 on R1236: Markov's inequality
F6614
Formulation 0
Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space such that
(i) $f : X \to [0, \infty]$ is an D5610: Unsigned basic Borel function on $M$
Let $\lambda \in (0, \infty)$ be a D5407: Positive real number.
Then \begin{equation} \mu(\{ x \in X : f(x) \geq \lambda \}) \leq \frac{1}{\lambda} \int_X f \, d \mu \end{equation}