Let (T,d) be a metric space and φ:ℝ+→ℝ an increasing, convex function with φ(0)=0. We prove that if m is a probability measure m on T which is majorizing with respect to d, φ, that is, $\mathcal{S}:=\sup_{x\in T}\int^{D(T)}_{0}\varphi^{-1}(\frac {1}{m(B(x,\varepsilon ))})\,d\varepsilon \textless\infty$ , then
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\[\mathbf{E}\sup_{s,t\in T}|X(s)-X(t)|\leq 32\mathcal{S}\]
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for each separable stochastic process X(t), t∈T, which satisfies $\mathbf{E}\varphi(\frac {|X(s)-X(t)|}{d(s,t)})\leq 1$ for all s, t∈T, s≠t. This is a strengthening of one of the main results from Talagrand [Ann. Probab. 18 (1990) 1–49], and its proof is significantly simpler.