Measures with common distribution function

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Let $\varphi: [0, \infty) → [0, \infty]$ be growing monotonously. $\tau_1$ and $\tau_2$ are two (finite) measures on $([0, \infty), B([0, \infty)))$ and $\varphi$ is their distribution function. how can i show, that $\tau_1 = \tau_2$?