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The Bernoulli space〔Elart von Collani (ed.), ''Defining the Science Stochastics'', Heldermann Verlag, Lemgo, 2004.〕 is a mathematical model for the transition from past to future in due consideration of uncertainty of future developments. The Bernoulli space is at the core of Bernoulli stochastics and represents the basis for reliable and accurate predictions and measurements. The Bernoulli space does not assume a "ideal world" as, for example, physics which is based on the belief in truth and causality. In contrast, the Bernoulli space admits human ignorance and cosmological randomness which both generate uncertainty. The Bernoulli Space as a mathematical model of change can therefore be regarded as the means for obtaining reliable and accurate predictions. ==Uncertainty== Before the model can be introduced, the term uncertainty〔Elart von Collani, Defining and Modeling Uncertainty, ''Journal of Uncertain Systems'' Vol.2, No.3, 202–211, 2008, ().〕 must be uniquely explained since in everyday speech it can have several inconsistent meanings. In everyday speech uncertainty may refer to determinate, but unknown facts, or to the indeterminate future that cannot be known as it does not exist so far. The difference between facts and future events is obvious, a fact is specified and if quantified has a fixed value, while a future event is indeterminate and therefore may or may not occur. A fact might be unknown, but nevertheless it is fixed. A future event cannot be known or unknown because it is subject to randomness and may occur or not occur. For the sake of a unique interpretation, uncertainty is explained here as the inability to predict a future development exactly. This inability is due to ignorance about the past and randomness about the future. Ignorance and randomness generate uncertainty and for describing uncertainty quantitatively both sources have to be taken into account. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bernoulli space」の詳細全文を読む スポンサード リンク
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