abstract:In measure theory and probability, the monotone class theorem connects monotone classes and sigma-algebras. The theorem says that the smallest monotone class containing an algebra of sets G is precisely the smallest σ-algebra containing G.
By using a fixedpointtheoremofmixedmonotoneoperatorsincone, this paperstudied a fourth-ordernonlinearsingularboundaryvalueproblem, namely a class of elastic beam equation.