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mean compact

Last-modified: 2010-09-08 (水) 00:34:54

Definition Edit

  • Let M be a subset of a linear topological space X. M is called mean compact if given any sequence imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5c%7bx_n%5c%7d%20%5c%5d%7d%25.png in M there is a point x in X such that imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20f%20%5cin%20X%5e*%20%5c%5d%7d%25.png implies imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5clim%7b%7d_n%5cinf%20f%28x_n%29%5cle%20f%28x%29%5cle%5clim%7b%7d_n%5csup%20f%28x_n%29%20%5c%5d%7d%25.png.

Reference Edit

  • Heron Sherwood Collins, Completeness and Compactness in Linear Topological Spaces, Transactions of the American Mathematical Society, Vol. 79, No. 1 (May, 1955), pp.256-280.