Extension of measures on two disjoint rings

Abstract

We present a method of starting with two measures μ₁ and μ₂ defined on disjoint rings R₁ and R₂ respectively, and defining another measure which is an extension of both μ₁ and μ₂. The method is a generalization of a classical method of extending a measure. An outer measure μ* is defined on a hereditary σ – ring H(R₁, R₂) which is a superset of both R₁ and R₂, and then a complete measure on the class of μ*-measurable sets that belong to H(R₁, R₂) is defined in terms of μ*.

Subject Classification:

• (2010) 28A12
• 28A05
• 28E99

Keywords:

• Hereditary σ – ring
• complete measure
• extension of measure