A-Integrable

A generalization of the Lebesgue integral. A measurable function is called -integrable over the closed interval if

$m{x:|f(x)|>n}=O(n^(-1)),$

(1)

where is the Lebesgue measure, and

(2)

exists, where

$[f(x)]_n={f(x) if |f(x)|<=n; 0 if |f(x)|>n.$

(3)

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Titchmarsh, E. C. "On Conjugate Functions." Proc. London Math. Soc. 29, 49-80, 1928.