Sentence examples for be a linear expectation from inspiring English sources

Let E be a linear expectation.

(mathcal{E} ) is a minimal member of (S^{mathrm{sl}}); (mathcal{E} ) is a linear expectation.

(mathcal{E}_{0} ) is a maximal member of S; (mathcal{E}_{0} ) is a linear expectation.

(mathcal{E}_{0} ) is a minimal member of S; (mathcal{E}_{0} ) is a linear expectation.

Then the following statements are equivalent: (i) (mathcal{E} ) is a minimal member of (S^{mathrm{sl}});   (ii) (mathcal{E} ) is a linear expectation.  .

Then the following two statements are equivalent: (i) (mathcal{E}_{0} ) is a maximal member of S;   (ii) (mathcal{E}_{0} ) is a linear expectation.  .

Then (mathcal{E}_{0}) is a minimal member of S if and only if (mathcal{E}_{0}) is a linear expectation.

We prove that (mathcal{E}) is a minimal member of S if and only if (mathcal{E}) is a linear expectation.

Then the following two statements are equivalent: (i) (mathcal{E}_{0} ) is a minimal member of S;   (ii) (mathcal{E}_{0} ) is a linear expectation.  .

We show that (mathcal{E}) is a minimal member of S if and only if (mathcal{E}) is a linear expectation with the same constraints as above, respectively.

We prove that, for a subset S of all convex expectations containing all linear expectations, (mathcal{E}) is a minimal member of S if and only if (mathcal{E}) is a linear expectation.