 The collection formula_8 is called tight (or sometimes uniformly tight) if, for any formula_11, there is a compact subset formula_12 of formula_3 such that, for all measures formula_14,

where formula_16 is the total variation measure of formula_17.Very often, the measures in question are probability measures, so the last part can be written as

If a tight collection formula_8 consists of a single measure formula_17, then (depending upon the author) formula_17 may either be said to be a tight measure or to be an inner regular measure.If formula_22 is an formula_3-valued random variable whose probability distribution on formula_3 is a tight measure then formula_22 is said to be a separable random variable or a Radon random variable.