# A-integral

From Encyclopedia of Mathematics

One of the generalizations of the Lebesgue integral, given by E. Titchmarsh [1] for the integration of functions conjugate to summable ones. A measurable function is called -integrable over if

and if

exists, where

The number is called the -integral. It is denoted by

#### References

[1] | E.G. Titchmarsh, "On conjugate functions" Proc. London Math. Soc. , 29 (1928) pp. 49–80 |

[2] | I.A. Vinogradova, "Generalized integrals and Fourier series" Itogi Nauk. Mat. Anal. 1970 (1971) pp. 65–107 (In Russian) |

**How to Cite This Entry:**

A-integral.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=A-integral&oldid=18741

This article was adapted from an original article by I.A. Vinogradova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article