KnowraContinuous mapping theoremLinked fromLinked fromThe 5 pages that link to Continuous mapping theorem, each with the reason it gives.All 5Related 5Convergence in probabilityRelated: It lets convergent random variables pass through continuous transformations.Convergence in distributionRelated: It derives new distributional limits by applying functions to convergent random variables.Portmanteau theoremRelated: It often combines with Portmanteau tests to establish convergence of transformed random variables.Slutsky's theoremRelated: It extends the theorem’s limit rules from sums and products to continuous transformations.Skorokhod representation theoremRelated: A represented almost-sure limit can yield distributional limits after applying suitable functions.