Explore BrainMass
Share

Explore BrainMass

    Showing a quotient space is a complete metric space; Finite measurable space; Symmetric difference; Equivalence relations

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Let (X,B,mu) be a complete, finite measuable space. For each C,D in B, set

    d(C,D) = mu (C / D)

    where C / D is the symmetric difference of C and D. We say that two measurable sets C,D are equivalent if d(C,D)=0 (this is an equivalence relation).

    Let E be the set of equivalence classes, and show that d introduces a metric on E and that (E,d) is a complete metric space.

    © BrainMass Inc. brainmass.com October 9, 2019, 5:32 pm ad1c9bdddf
    https://brainmass.com/math/finite-element-method/60530

    Attachments

    Solution Summary

    Showing a quotient space is a complete metric space; Finite measurable space; Symmetric difference; Equivalence relations are investigated. The solution is detailed and well presented.

    $2.19