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Last-modified: 2010-12-28 (火) 22:32:24

Definition Edit

A Borel measure μ on a topological space X is called τ-additive if for every increasing net of open sets U_i in X, one has the equality imgtex.fcgi?%5bres=100%5d%7b$%7c%5cmu%7c%28%5ccup_%7bi%5cin%20I%7dU_i%29=%5clim_i%20%7c%5cmu%7c%28U_i%29$%7d%25.png
If the above equality holds for all nets with imgtex.fcgi?%5bres=100%5d%7b$%5ccup_%7bi%5cin%20I%7dU_i=X$%7d%25.png, μ is called τ_0-additive of weakly τ-additive.

Reference Edit

Vladimir Igorevich Bogachev, Measure Theory, Springer.