Let $X \in \text{Random}[0, \infty]$ be a D5101: Random unsigned basic number.
Let $\lambda > 0$ be a D993: Real number.

According to result R4145: Binary union is an upper bound to both sets in the union, we have the inclusion $$\begin{equation} \{ X > \lambda \} \subseteq \{ X > \lambda \} \cup \{ X = \lambda \} = \{ X \geq \lambda \} \end{equation}$$ Now, applying results

(i)	R2090: Isotonicity of probability measure
(ii)	R2016: Probabilistic Markov's inequality

we conclude with $$\begin{equation} \mathbb{P}(X > \lambda) \leq \mathbb{P}(X \geq \lambda) \leq \frac{1}{\lambda} \mathbb{E}(X) \end{equation}$$ $\square$