Sentence examples for measure on mathbb from inspiring English sources

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

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}).

Here the integral is with respect to Lebesgue measure on (mathbb {R}^{2}), and the integrand is a conditional expectation.

For every h>0, q(h,·) is a probability density function with respect to the Lebesgue measure on (mathbb {R}).

The functions q(h,·) are probability density functions with respect to the Lebesgue measure on (mathbb {R}).

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.

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

Then, (tilde varphi ) is a strongly time consistent dynamic LM-measure on (mathbb {V}^{infty }).

Now, let us present the counterpart of Proposition 4. Let φ be a dynamic LM-measure on (mathbb {V}^{p}), which is independent of the past.

The next result is the counterpart of Proposition 1 and Proposition 2. Let φ be a dynamic LM-measure on (mathbb {V}^{p}).