In the paper, we investigate a one-to-one correspondence between n-dimensional observables and n-dimensional spectral resolutions with values in a kind of a lexicographic form of quantum structures like perfect MV-algebras or perfect effect algebras. The multidimensional version of this problem is more complicated than a one-dimensional one because if our algebraic structure is k-perfect for $k>1$, then even for the two-dimensional case we have more characteristic points. The obtained results are also applied to existence of an n-dimensional meet joint observable of n one-dimensional observables on a perfect MV-algebra. The results are divided into two parts. In Part I, we present notions of n-dimensional observables and n-dimensional spectral resolutions with accent on lexicographic type effect algebras and lexicographic MV-algebras. We concentrate on characteristic points of spectral resolutions and the main body is in Part II where one-to-one relations between observables and spectral resolutions are presented.

在本文中，我们研究了n维可观测量和n维光谱分辨率之间的一一对应关系，其值是一种量子结构的字典形式，如完美 MV 代数或完美效应代数。这个问题的多维版本比一维问题更复杂，因为如果我们的代数结构是k完美的$ķ>1$，那么即使是二维的情况，我们也有更多的特征点。所获得的结果也适用于在完美 MV 代数上存在 n 个一维可观测量的n维交联可观。结果分为两部分。在第一部分中，我们提出了n维可观测量和n维光谱分辨率的概念，并强调词典类型效应代数和词典 MV 代数。我们专注于光谱分辨率的特征点，主体在第二部分，其中介绍了可观测量和光谱分辨率之间的一对一关系。