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In this paper we prove a L\'evy-Ottaviani type of property for the Bernoulliprocess defined on an interval. Namely, we show that under certain conditionson functions $(a_i)_{i=1}^{n}$ and for independent Bernoulli random variables$(\varepsilon_i)_{i=1}^{n}$, $\mathbb{P}(\sup_{t\in[0,1]}\sum^n_{i=1}a_i(t)\varepsilon_i\geq c)$ is dominated by$C\mathbb{P}(\sum^n_{i=1}a_i(1)\varepsilon_i\geq1)$, where $c$ and $C$ areexplicit numerical constants independent of $n$. The result is a partial answerto the conjecture of W. Szatzschneider that the domination holds with $c=1$ and$C=2$.

A L\'evy-Ottaviani type inequality for the Bernoulli process on an interval