Lebesgue Integral

The Lebesgue Integral is defined in terms of upper and lower bounds using the Lebesgue Measure of aSet. It uses a Lebesgue Sum where is the value of the function insubinterval , and is the Lebesgue Measure of the Set of points for which values areapproximately . This type of integral covers a wider class of functions than does the Riemann Integral.

References

Kestelman, H. ``Lebesgue Integral of a Non-Negative Function'' and ``Lebesgue Integrals of Functions Which Are Sometimes Negative.'' Chs. 5-6 in Modern Theories of Integration, 2nd rev. ed. New York: Dover, pp. 113-160, 1960.

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