Abstract
Relative weakly compact sets and weak convergence in variable exponent Lebesgue spaces {L^{p(cdot )}(Omega )} for infinite measure spaces (Omega ,mu ) are characterized. Criteria recently obtained in [14] for finite measures are here extended to the infinite measure case. In particular, it is showed that the inclusions between variable exponent Lebesgue spaces for infinite measures are never L-weakly compact. A lattice isometric representation of {L^{p(cdot )}(Omega )} as a variable exponent space L^{q(cdot )}(0,1) is given.
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