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In this work the problem about an existence of non-measurable automorphismsof Lie groups finite and as well infinite dimensional over the field of realnumbers and also over the non-archimedean local fields is investigated.Non-measurability of automorphisms is considered relative to real-valuedmeasures and also measures with values in non-archimedean local fields. Theirexistence is proved and a procedure for their construction is given. Theirapplication for a construction of non-measurable irreducible unitaryrepresentations is demonstrated.

Non-measurable automorphisms of Lie groups relative to the real- and non-archimedean-valued measures