关键词： 空间构造出来的.概率度量空间, 概率赋范空间, 概率度量群, 概率仿射度量空间, 概率赋准范空间, 拓扑线性空间, 拓扑群

Abstract: The authors give the definitions of PMG and LPM space and  introduce a special LPM space,which is called PQN space.Then a special PM space named APM space is also introduced.In each APM space,an linear structure can be constructed such that this PM space is an LPM space.An example of APM space which is constructed by a non-topological vector PN space is given.

Key words: PM space, PN space, PMG, APM space；PQN space, topological vector space, topological group