# In Probability, what does $\leq_{ST}$ mean? (context in question)

It is used in the following way, given subsets of the sample space $$A_1, \cdots, A_n \subset \Omega$$ such that $$\mathbb{P}(A_i) \leq \theta$$.

Now define i.i.d. Bernoulli r.v.s $$B_i \sim Ber(\theta)$$, then $$(\chi_{A_1} , \cdots, \chi_{A_n}) \leq_{ST} (B_1, \cdots, B_n).$$

What does this $$\leq_{ST}$$ mean precisely?

• Probably "stochastic domination." I don't remember the definition though. – Will M. Apr 10 at 18:53
• It's called stochastic order, just look it up. – dnqxt Apr 10 at 18:58
• Thank you all . – Xiao Apr 10 at 19:28