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A1672
**Title: **The limits of measurement
**Authors: **Ioannis Paraskevopoulos - Universidad Pontificia Comillas (Spain) **[presenting]**

**Abstract: **The focus is on the dependence of the unknown stochastic solution on the known stochastic chain in Banach space. We extend the limits of computation beyond Hilbert space, as Banach space is somewhere in between the Hilbert and another space endowed with a measure but without a norm. In particular, we examine whether the evolution process depends on its known history. We argue that multidimensional integration has its dual in reflexive Banach space if the solution obeys the functional central limit theorem and its error is between the limits of dilation and erosion. Hence there is an isomorphism for closed and semi-open intervals and the desired inner product to define the orthogonality conditions for the open interval $\left[0,1\right)$. One possible scenario will be, as previously suggested, no model exists and reversibility will be unattainable as it would map to infinite possible initial points of the past. In this case all strong solutions will be of this type, $S_k=\left(\prod_{-\infty}^{k}\xi_j\right)V$. Where $V$ is an independent process. We derive the orthogonality conditions and show that the unknown stochastic unique solution would depend on the observable history of the sequence, as $S_m=\prod_{-\infty}^{m}\rho_j S_{m-1}$.