Summable function

A function , where is a space with a non-negative measure, for which the Lebesgue integral is defined and finite. The set of summable functions forms a linear subspace of the space of measurable functions. Taking the absolute value of a function and the maximum and minimum of a finite system of functions does not lead outside . If , then is closed in the sense of uniform convergence.

Comments

A standard notation for the space of summable or Lebesgue integrable functions on is or (or , ).

References

[a1]	W. Rudin, "Real and complex analysis" , McGraw-Hill (1966) pp. 24
[a2]	G.E. Shilov, B.L. Gurevich, "Integral, measure, and derivative: a unified approach" , Dover, reprint (1977) pp. 29ff (Translated from Russian)