The following result gives equivalent conditions for the integrability of S ( T M ).
In Section 3, we give equivalent conditions for the existence of nth iterative roots and their expressions.
In developing their properties, Ikegami gave several equivalent conditions that force them to have an integral representation even with respect to minimal representing measures onthe boundary of P in [6].
We give some equivalent conditions in terms of generator, resolvent and semigroup.
First, we give several equivalent conditions for the continuity of δg ∗ μ in g ∈ G. Then for a quasi-invariant and ergodic probability measure on a measurable group, we prove a zero-one law for translated subgroups, which is a natural extension of Kallianpur′s zero-one law for Gaussian measures, and apply it to the Wiener measure on a loop group.
Lemma 5 in [8] gives seven equivalent conditions connected with BroC.
As stated in Section 1, Lemma 5 in Jachymski [8] gives seven equivalent conditions connected with BroC.
First, we give some equivalent conditions for the n th derivative of Q K ( p, q ) Open image in new window spaces.
They gave some equivalent conditions, under which a derivation is isotone for lattices with a greatest element, modular lattices and distributive lattices, respectively.
Furthermore, we give four equivalent conditions on the n-dimensional Jensen inequality for g-evaluations induced by backward stochastic differential equations with non-uniform Lipschitz coefficients in (L^{p} (Omega,{mathcal{F}}, ({mathcal {F}}_{t} )_{0leq tleq T},P )) ((1< pleq2)).
In Section 3, we give four equivalent conditions on the 1-dimensional Jensen inequality and the n-dimensional ((n>1)) Jensen inequality for g-evaluations induced by BSDEs with non-uniform Lipschitz coefficients in (L^{p} (Omega,{mathcal{F}}, ({mathcal {F}}_{t} )_{0leq tleq T},P )) ((1< pleq2)), respectively.
