Geodesic
Tempered processes and a Riesz decomposition for some martingales in the limit
Glasgow mathematical journal, Tome 22 (1981) no. 1, pp. 9-17

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Several papers have appeared in the past few years which have explored the topic of the Riesz decomposition for amarts. Such a decomposition for amarts enjoys several special properties. See [5, p. 208–209]. While it has been proved in [6] that not every martingale in the limit has a Riesz decomposition “in the weakest form assuring uniqueness” it is the major objective of this paper to characterize a class of martingales in the limit which is strictly larger than the class of amarts but enjoys all the properties of the decomposition for amarts. 
Blake, Louis H. Tempered processes and a Riesz decomposition for some martingales in the limit. Glasgow mathematical journal, Tome 22 (1981) no. 1, pp. 9-17. doi: 10.1017/S0017089500004420
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