Sentence:  Using a result of Dranishnikov and Smith we prove that, under some conditions, the asymptotic power dimension of a proper metric space coincides with the dimension of its <WSD>subpower</WSD> corona. 
Meaning of the word marked with <WSD> tags:  A type of function such that for every exponent a, there is a small integer ε such that for any positive value x less than ε, its image lies between xa and x-a .