## Minimal excessive measures and functions

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- by E. B. Dynkin
- Trans. Amer. Math. Soc.
**258**(1980), 217-244 - DOI: https://doi.org/10.1090/S0002-9947-1980-0554330-5
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## Abstract:

Let*H*be a class of measures or functions. An element

*h*of

*H*is minimal if the relation $h = {h_1} + {h_2}$, ${h_1}$, ${h_2} \in H$ implies that ${h_1}$, ${h_2}$ are proportional to

*h*. We give a limit procedure for computing minimal excessive measures for an arbitrary Markov semigroup ${T_t}$ in a standard Borel space

*E*. Analogous results for excessive functions are obtained assuming that an excessive measure $\gamma$ on

*E*exists such that ${T_t}f = 0$ if $f = 0$ $\gamma$-a.e. In the Appendix, we prove that each excessive element can be decomposed into minimal elements and that such a decomposition is unique.

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## Bibliographic Information

- © Copyright 1980 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**258**(1980), 217-244 - MSC: Primary 60J50; Secondary 28D99, 47D07
- DOI: https://doi.org/10.1090/S0002-9947-1980-0554330-5
- MathSciNet review: 554330