Sentence examples for easy proof of from inspiring English sources
The easy proof of the next lemma is given in [11].
We now examine an easy proof of Caristi's original theorem based on Zorn's lemma.
An easy proof of the John-Nirenberg inequality is provided by merely using the Calderón-Zygmund decomposition.
To show an easy proof of the sharpness, we employ a lemma implicit in [25] as the key of the argument.
The geometric picture leads to an easy proof of the following identity: Let (X,Yin mathbf{P}_n), and (t_0, t_1in {mathord {{mathbb {R}}}}).
Stimulated by these works, we give, in this paper, an easy proof of the John-Nirenberg inequality by using the Calderón-Zygmund decomposition only.
In Section 3, alternate and easy proofs of results [[13], Lemmas 2.1, 2.10] are discussed.
Still, our semantics provides decision procedures for all the systems investigated, as well as easy proofs of important proof-theoretical properties of them.
Second, and as a consequence of the previous fact, we present very easy proofs of some of the self-improving properties of the generalized Poincaré inequalities studied by B. Franchi, C. Pérez and R.L. Wheeden in [9], and by P. MacManus and C. Pérez in [21].
But there are no known "easy" proofs of the inequality for the full range of values, the main difficulty being near small values of s, e.g., between 2 and 4 [2].
An easier proof for the orthogonality of the Plackett and Burman designs with prime power run numbers is also presented.
