Signed measures, defined in Section III.l, have values either in (-∞,+∞] or [-∞,+∞), to avoid the possibility of adding +∞ to -∞. It will be shown in Section 2 that a signed measure is actually bounded on the side where it is finite. For a signed measure space (S, S,λ,), the signed measure λ has its values in (-∞,+∞] if and only if λ(S) > -∞, its values in [-∞,+∞) if and only if λ(S) < +∞, and λ is finite valued if and only if λ(S) is finite.
KeywordsMeasure Space Signed Measure Measurable Subset Finite Measure Jordan Decomposition
Unable to display preview. Download preview PDF.