This book explores a number of new applications of invariant
quasi-finite diffused Borel measures in Polish groups for a
solution of various problems stated by famous mathematicians (for
example, Carmichael, Erdos, Fremlin, Darji and so on). By using
natural Borel embeddings of an infinite-dimensional function space
into the standard topological vector space of all real-valued
sequences, (endowed with the Tychonoff topology) a new approach for
the construction of different translation-invariant quasi-finite
diffused Borel measures with suitable properties and for their
applications in a solution of various partial differential
equations in an entire vector space is proposed.
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