Sentence examples for equivalent the statement from inspiring English sources

The statement of the lemma is equivalent the statement that if the prey goes to extinction, then the predator also goes to extinction.

"The transaction will provide customers with access to high quality and more efficient products and services, and an opportunity to reduce their cost per barrel of oil equivalent," the statement said.

It is shown that the fan principle is equivalent to the statement that the unit interval [0,1] has the Heine-Borel property, and from this many other equivalents are derived.

The celebrated Riemann hypothesis is equivalent to the statement that Ξ ( z ) has only real zeros.

This is equivalent to the statement that the curve representing the transport numbers as a function of composition crosses the diagonal ("inversion point").

This is, in fact, equivalent to the statement that the occurrence probability of ESF is almost 100% for this PRE value.

Then the discrete representation (3) of the differential problem (1 - 2) is equivalent to the statement that the linear transformation A maps x into y.

This is equivalent to the statement that any sequence x = ( x n ) of points in E has a convergent subsequence whose limit is in E.

It is equivalent to the statement that in L 1, ({lim }_{nrightarrow infty }mathbb {E}[|Z_{n+1}-E_{n}|] = 0) which implies E[|Z ∞ −E ∞ |]=0.

Since Φ is affine, formula (4.4) implies g(x 2=g(x 2) for all, which is equivalent to the statement that is an algebra isomorphism.

Thus, Theorem 2 is equivalent to the statement that the PA (18) with a proper λ>0 can be optimal for problem (10) if and only if energy should be exhausted at the end of the timeslot.