Thomas–Lehmann Theorem

The Thomas–Lehmann Theorem states that if a statistical distribution (describing data) can be expressed as a mixture (combination) of simpler distributions, then the properties called "monotone likelihood ratio" are preserved. This means that when you mix distributions with a certain orderliness in how they react to data, the combined distribution maintains that orderliness. It's important in statistics for understanding how different data sources combine and ensuring that patterns or distinctions remain clear and consistent when combined.