一個可分配且有最小跟最大元素的束L可以嵌入到C(S)，其中S是一個緊緻豪斯多夫空間。如果L是一個布林代數，則L有表示式可以用來擴張在L上有界變分的valuation變成一個定義在S的鮑萊爾代數上的Radon測度。

A distributive lattice L with smallest and largest elements can be embedded in C(S) for some compact Hausdorff space S. When L is a boolean algebra, L has a representation can be used to extend the valuations of bounded variation on L to Radon measures on the Borel algebra of S.

0 Introduction                                          1
1 Preliminaries                                         2  
  1.1 Basic Concepts of Lattices                        2
  1.2 Refinement Theorem of Two Finite Chains           4
  1.3 Vector Lattices                                   7
  1.4 Normed Lattices                                  10
  1.5 Some Concepts of Functional Analysis             11
  1.6 Abstract L-Space and Abstract M-Space            12
2 Embedding Distributive Lattices in Vector Lattices   15
3 Representation of Lattices and Extension of Measures 23
References                                             29

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