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IV: 15, 170-194, LNM 124 (1970)

**MOKOBODZKI, Gabriel**

Densité relative de deux potentiels comparables (Potential theory)

The main problem considered here is the following: given a transient resolvent $(V_{\lambda})$ on a measurable space, a finite potential $Vg$, an excessive function $u$ dominated by $Vg$ in the strong sense (i.e., $Vg-u$ is excessive), show that $u=Vf$ for some $f\leq g$, and compute $f$ by some ``derivation'' procedure, like $\lim_{\lambda\rightarrow\infty} \lambda(I-\lambda V_{\lambda})\,u$

Comment: The main theorem and the technical tools of its proof have been landmarks in the potential theory of a resolvent, though in the case of the resolvent of a good Markov process there is a simple probabilistic proof of the main result. Another exposition can be found in*Séminaire Bourbaki,* **422**, November 1972. See also Chapter XII of Dellacherie-Meyer, *Probabilités et potentiel,* containing new proofs due to Feyel

Keywords: Resolvents, Strong ordering, Lebesgue derivation theorem

Nature: Original

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IV: 16, 195-207, LNM 124 (1970)

**MOKOBODZKI, Gabriel**

Quelques propriétés remarquables des opérateurs presque positifs (Potential theory)

A sequel to the preceding paper 415. Almost positive operators are candidates to the role of derivation operators relative to a resolvent

Comment: Same as 415

Keywords: Resolvents, Strong ordering, Lebesgue derivation theorem

Nature: Original

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V: 21, 211-212, LNM 191 (1971)

**MEYER, Paul-André**

Deux petits résultats de théorie du potentiel (Potential theory)

Excessive functions are characterized by their domination property over potentials. The strong ordering relation between two functions is carried over to their réduites

Comment: See Dellacherie-Meyer*Probability and Potentials,* Chapter XII, \S2

Keywords: Excessive functions, Réduite, Strong ordering

Nature: Original

Retrieve article from Numdam

Densité relative de deux potentiels comparables (Potential theory)

The main problem considered here is the following: given a transient resolvent $(V_{\lambda})$ on a measurable space, a finite potential $Vg$, an excessive function $u$ dominated by $Vg$ in the strong sense (i.e., $Vg-u$ is excessive), show that $u=Vf$ for some $f\leq g$, and compute $f$ by some ``derivation'' procedure, like $\lim_{\lambda\rightarrow\infty} \lambda(I-\lambda V_{\lambda})\,u$

Comment: The main theorem and the technical tools of its proof have been landmarks in the potential theory of a resolvent, though in the case of the resolvent of a good Markov process there is a simple probabilistic proof of the main result. Another exposition can be found in

Keywords: Resolvents, Strong ordering, Lebesgue derivation theorem

Nature: Original

Retrieve article from Numdam

IV: 16, 195-207, LNM 124 (1970)

Quelques propriétés remarquables des opérateurs presque positifs (Potential theory)

A sequel to the preceding paper 415. Almost positive operators are candidates to the role of derivation operators relative to a resolvent

Comment: Same as 415

Keywords: Resolvents, Strong ordering, Lebesgue derivation theorem

Nature: Original

Retrieve article from Numdam

V: 21, 211-212, LNM 191 (1971)

Deux petits résultats de théorie du potentiel (Potential theory)

Excessive functions are characterized by their domination property over potentials. The strong ordering relation between two functions is carried over to their réduites

Comment: See Dellacherie-Meyer

Keywords: Excessive functions, Réduite, Strong ordering

Nature: Original

Retrieve article from Numdam