Sentence examples for measures on mathbb from inspiring English sources

Then let (mu_{t}^{ (N )}) be a sequence of symmetric probability measures on (mathbb {R}^{dtimes N}), where N is the number of neurons in the system.

As in the case of random variables, strong time consistency is usually considered for dynamic monetary risk measures on (mathbb {V}^{infty }).

Let (mu ) and (nu ) be two probability measures on (mathbb {R}^n) with (mu ) absolutely continuous with respect to Lebesgue measure.

Let N be the set of all counting measures on (mathbb {R}^{d}) which are finite on any bounded Borel set and for which the measure of a point is at most 1.

Let (h :mathbb{R }rightarrow [0,infty )) be compactly supported and let ({varvec{mu }}={mu _n}_{n=0}^infty ) be a sequence of Borel measures on (mathbb T ^q) with nested support. Let (f in cap _{n=0}^infty L^1(mu _n)).

If φis a dynamic one-step LM-measure on (mathbb {V}^{p}), which is μ-acceptance (resp. μ-rejection) time consistent, then φ is weakly acceptance (resp. weakly rejection) time consistent.

The measure on (mathbb {S}^{1}) used in this formula has total mass one.

Let ({varphi ^{x}}_{xin mathbb {R}_) be a decreasing family14 of dynamic LM-measures on (mathbb {V}^{p}).

The measure (mu _q^*) denotes the Lebesgue measure on (mathbb T ^q) normalized to (1).

Suppose μ is a positive measure on (mathbb {R}_) and it has an atom (x_{0}).

Let φ be a dynamic LM-measure on (mathbb {V}^{p}).