Talk:Kolmogorov's three-series theorem

convergence versus "less than infinity"[edit]

Surely the two mean the same for series of positive terms. So why does Condition 2 have "converges", while Conditions 1 and 3 have "less than infinity"? DavidHobby (talk) 13:39, 2 November 2010 (UTC)[reply]

Maybe because it's more elegant to write $<\infty \,$ $<\infty \,$ than to write converges :-) Albmont (talk) 16:02, 18 February 2011 (UTC)[reply]
- Agreed, there's no issue here. These are commonly used interchangeably.

motion to capitalize title[edit]

It's a proper noun. Otherwise, what accounts for the unusual hyphen use? Elizabethevangeline (talk) 06:55, 14 December 2013 (UTC)[reply]

Notation could be defined a little bit better[edit]

This line, for example: Yn:= Xn1{|X|n ≤ A}

Is this magic "1" meant to be an indicator function? i.e., the Xn for which the absolute value of Xn is less than some A?

I feel that Wikipedia should be clearer than the theorems/technical content it is attempting to introduce, otherwise there's little gain.

107.3.128.7 (talk) 05:58, 15 June 2016 (UTC)[reply]

A bit of interpretation[edit]

K3S can be interpreted as an implication of symmetry. Infinite sum of any digital signal is converging iff a high-pass filter have convergent sums of the three mentioned measures. It is symmetry on the remainder set which is a low-pass filter and does not need to be finite. If it was finite it is already proved that is sum of any finite set is converging. It means that if the signal sequence overall behave vaguely symmetric around the origin. i.e. The three series are the information through two scales with regard to state of convergence. It does not matter what lower scale behaviors show, The larger scale phenomena only receives information with respect to $p,\mu ,\sigma$ and if a scale phenomena do not alter the three measures of inter-scale communication for convergence, they also can not alter the state of the convergence of the original series. i.e. convergence is invariant with respect to all types of low scale behavior of the system if they happen within some finite domain. Miladkiaee (talk) 02:02, 11 November 2019 (UTC)[reply]