Thus, if the limit of some sequence in is less than , then the limit is also in .
The values of the sequence Hn - ln(n) decrease monotonically towards the limit
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In mathematics, particularly functional analysis, the Dunford–Schwartz theorem, named after Nelson Dunford and Jacob T. Schwartz states that the averages of powers of certain norm-bounded operators on converge in a suitable sense.
An unpublished argument of Fred Galvin shows that the quantity inside this limit is nonincreasing for n ≥ k, and so the limit exists.