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Fedor Petrov
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Yes, this is called 'majorization' or 'second order stochastic dominance' of measures (first term is used in analysis, second in probability). The idea is very simple: we partition the measure $\mu$ on several summands $\mu=\sum \mu_i$ and replace each $\mu_i$ to its mean value.

Fedor Petrov
  • 108.9k
  • 9
  • 264
  • 459