*Definition [#w9893387]
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 &ref(http://www.eaflux.com/imgtex/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 &ref(http://www.eaflux.com/imgtex/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 [#b594f79a]
Vladimir Igorevich Bogachev, ''Measure Theory'', Springer.