This article is cited in 4 papers

On the interrelation of $A$- and $B$-integrals

B. V. Pannikov


Abstract: Using the law of large numbers, the author shows that on the set of measurable functions the $A$-integral is an extension of the $B$-integral. Also, by using a form of the law of large numbers, he defines an integral that includes the Lebesgue integral and has, for any given function whose positive or negative part is not Lebesgue integrable, any preassigned number as its integral over (0,1).
Bibliography: 12 titles.

UDC: 517.5

MSC: Primary 26A39; Secondary 26A42, 60F05

Received: 16.11.1984

 English version: Mathematics of the USSR-Sbornik, 1987, 57:2, 421–435

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