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Salvo Tringali's user avatar
Salvo Tringali's user avatar
Salvo Tringali
  • Member for 13 years, 5 months
  • Last seen this week
  • Shijiazhuang, Hebei, China
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answered
Who needs a symmetric upper asymptotic density on the integers?
revised
Sums of two squares: positive lower density?
Fixed a couple more of typos
revised
Sums of two squares: positive lower density?
Added a condition I had forgot in the definition on an upper quasi-density
revised
Sums of two squares: positive lower density?
deleted 7 characters in body
revised
Sums of two squares: positive lower density?
added 2 characters in body
revised
Sums of two squares: positive lower density?
Added a generalization
comment
Ref. request: Additive probability measure on $\mathcal P({\bf N})$ supplies subset of $\mathbf R$ without Baire property
Wonderful! Thank you very much, Martin. Just a picky detail: I think the correct reference for [1972c] should be: D. Pincus, "The strength of the Hahn-Banach theorem", 203-248 in: A. E. Hurd and P. Loeb (eds.), Victoria Symposium on Nonstandard Analysis, Lecture Notes in Math. 369, Springer, 1974 (see link.springer.com/book/10.1007/BFb0065992). I mean, the conference took place in 1972, but the volume was published in 1974 (not in 1973).
accepted
Ref. request: Additive probability measure on $\mathcal P({\bf N})$ supplies subset of $\mathbf R$ without Baire property
revised
Ref. request: Additive probability measure on $\mathcal P({\bf N})$ supplies subset of $\mathbf R$ without Baire property
added some information
revised
Ref. request: Additive probability measure on $\mathcal P({\bf N})$ supplies subset of $\mathbf R$ without Baire property
added 4 characters in body
asked
Ref. request: Additive probability measure on $\mathcal P({\bf N})$ supplies subset of $\mathbf R$ without Baire property
accepted
Who needs a symmetric upper asymptotic density on the integers?
comment
Who needs a symmetric upper asymptotic density on the integers?
This is far more than what I was hoping for. Thank you so much!
revised
Who needs a symmetric upper asymptotic density on the integers?
edited title
revised
Who needs a symmetric upper asymptotic density on the integers?
Changed the title; new update
revised
Who needs a symmetric upper asymptotic density on the integers?
added 79 characters in body
revised
Who needs a symmetric upper asymptotic density on the integers?
Update
revised
Nonnegative integers represented by $\prod_{i=1}^m \sum_{j=1}^n a_{i,j} x_j $, where the $a_{i,j}$ are positive integers
Fixed another typo
comment
Nonnegative integers represented by $\prod_{i=1}^m \sum_{j=1}^n a_{i,j} x_j $, where the $a_{i,j}$ are positive integers
Sorry for the delay in replying to the comments. #Soufiane: Let me try to edit the OP and clarify my request. #Gerhard: In fact, I'm mainly interested in the case $n=2$, but I've a feeling that it doesn't make a big difference, and that's why I've phrased the question in its current form. Btw, it is likely that the assumption on $A$ being square and invertible is, on a second thought, completely useless, so I'm going to remove it.
revised
Nonnegative integers represented by $\prod_{i=1}^m \sum_{j=1}^n a_{i,j} x_j $, where the $a_{i,j}$ are positive integers
Fixed a typo
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