It is shown that Gelfand transforms of elements f Î L¥ (m){fin L^{infty} (mu)} are almost constant at almost every fiber P-1({x}){Pi^{-1}({x})} of the spectrum of L ∞(μ) in the following sense: for each f Î L¥ (m){fin L^{infty} (mu)} there is an open dense subset U = U(f) of this spectrum having full measure and such that the Gelfand transform of f is constant on the intersection P-1({x})ÇU{Pi^{-1}({x})cap U}. As an application a new approach to disintegration of measures is presented, allowing one to drop the usually taken separability assumption.
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机译：结果表明，在几乎每条光纤P -1 上，元素fÎL ¥（m）{fin L ^ {infty}（mu）}的Gelfand变换几乎恒定。 L ∞（μ）的频谱的（{x}）{Pi ^ {-1}（{x}）}在以下意义上：对于每个fÎL ¥（m）{fin L ^ {infty}（mu）}，该频谱有一个开放的密集子集U = U（f），具有完整的度量，因此f的Gelfand变换在交点P -1 （{x}）ÇU{Pi ^ {-1}（{x}）cap U}。作为一种应用，提出了一种分解度量的新方法，允许人们放弃通常采用的可分离性假设。
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