A real measure 
on a measurable space 
is a finite signed measure,
equivalently a complex measure whose values are
all real numbers (Rudin 1987, p. 119). Its total variation satisfies 
. A general signed
measure may also take one of the values 
and 
(Hunter 2011, pp. 70-71).
Real Measure
See also
Complex Measure, Jordan Measure Decomposition, Measure, Positive Measure, Signed Measure, Total VariationExplore with Wolfram|Alpha
References
Hunter, J. K. Measure Theory. Lecture notes, pp. 70-74, 2011. https://www.math.ucdavis.edu/~hunter/measure_theory/measure_notes.pdf.Rudin, W. Real and Complex Analysis, 3rd ed. New York: McGraw-Hill, pp. 118-119, 1987.Referenced on Wolfram|Alpha
Real MeasureCite this as:
Weisstein, Eric W. "Real Measure." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RealMeasure.html