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Lifting Theory was first introduced by John von Neumann in his (1931) pioneering paper (answering a question raised by Alfréd Haar ), followed later by Dorothy Maharam’s (1958) paper, and by A. Ionescu Tulcea and C. Ionescu Tulcea’s (1961) paper. Lifting Theory was motivated to a large extent by its striking applications; for its development up to 1969, see the Ionescu Tulceas' work and the monograph, now a standard reference in the field. Lifting Theory continued to develop after 1969, yielding significant
A lifting on a measure space ( X , Σ, μ) is a linear and multiplicative inverse
of the quotient map
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