We study Cegrell classes on compact Kähler manifolds. Our results generalize some theorems of Guedj and Zeriahi (from the setting of surfaces to arbitrary manifolds) and answer some open questions posed by them.

We discuss the existence of the current $g^{k}T$, $k\in \mathbb{N}$ for positive and closed currents $T$ and unbounded plurisubharmonic functions $g$. Furthermore, a new type of weighted Lelong number is introduced under the name of weight $k$ Lelong number.

On montre l’existence d’applications rationnelles $f:{\mathbb{P}}^k\to {\mathbb{P}}^k$ telles que$f$ est algébriquement stable  : pour tout $n\ge 0$, $deg{f}^{\circ n}={(degf)}^n$,il existe un unique courant positif fermé $T$ de bidegré $(1,1)$ vérifiant $f^{*}T=d·T$ et ${\int }_{{\mathbb{P}}^k}T\wedge {\omega }^{k-1}=1$ où $\omega$ est la forme de Fubini-Study sur ${\mathbb{P}}^k$ et$T$ est pluripolaire  : il existe un ensemble pluripolaire $X\subset {\mathbb{P}}^k$ tel que ${\int }_{X}T\wedge {\omega }^{k-1}=1$