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We establish the bilateral exact reciprocal interrelations between a tailbehavior of a measurable functions and its norm in the suitable Grand LebesgueSpace (GLS) as well as Orlicz one, builded over the set with infinite measure.  We bring also some examples in order to illustrate the exactness of offeredestimates.

Tail estimations for functions belonging to Grand Lebesgue Spaces builded on the set with infinite measure