Measure, Integration & Real Analysis · Problem 9B.8
Linear Maps on Hilbert Spaces — Sheldon Axler
Mathematics — Measure Theory · jordan-decomposition-positive-negative-parts
Problem
Suppose ν is a real measure on a measurable space (X,S). Prove that
ν+(E)=sup{ν(D):D∈S and D⊆E}
and
ν−(E)=−inf{ν(D):D∈S and D⊆E}
for all E∈S.
Browse the problem library