SkorohodsRepresentationTheorem

Skorohod's theorem is a mathematical result in probability theory named after the Soviet mathematician Anatoliy Skorohod. The theorem provides a representation for the weak convergence of probability measures on a metric space. It states that if a sequence of random variables or probability measures converges weakly (in distribution) to a limiting random variable or probability measure, then there exists another sequence of random variables, defined on a common probability space, that converges almost surely to the limit.

The theorem has important implications in various areas of probability theory and stochastic processes, such as convergence of stochastic processes, weak convergence of measures, and functional analysis.

To pronounce "Skorohod," say it as "skuh-ROH-hod" (rhyming with "score a rod"). The emphasis is on the second syllable, and the "h" in the last syllable is pronounced like the "h" in "hot."