The major reason for use of superadditive sequences is the following lemma due to Fekete.
For every superadditive sequence the limit exists and is equal to .
Similarly, a function is superadditive if
The analogue of Fekete lemma holds for superadditive functions as well.
There are extensions of Fekete lemma that do not require (1) to hold for all and . There are also results that allow one to deduce the rate of convergence to the limit whose existence is stated in Fekete lemma if some kind of both super- and subadditivity is present. A good exposition of this topic may be found in .
- 1 György Polya and Gábor Szegö. Problems and theorems in analysis, volume 1. 1976. http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0338.00001Zbl 0338.00001.
- 2 Michael J. Steele. Probability theory and combinatorial optimization, volume 69 of CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM, 1997. http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0916.90233Zbl 0916.90233.
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