Equipartitioning common domains of non-atomic measures
If \(\mu_ 1,\mu_ 2,...,\mu_ n\) are non-atomic finite measures on the same measure space (X,\({\mathcal F})\), then there is a measurable partition \(A_ 1,...,A_ n\) of X such that \(\mu_ i(A_ i)\geq n^{- 1}h(\|\mu_ 1\|,...,\|\mu_ n\|)\) for all \(i=1,...,n\), where \(h(a_ 1,...,a_ n)\) is the harmonic mean \(n(a_ 1^{- 1}+...+a_ n^{-1})^{-1}\) of \(a_ 1,...,a_ n\) and \(\|\mu \|\) is the total variation of \(\mu\) ; moreover, this bound is best possible.
scientific article; zbMATH DE number 3874310