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nLab > Latest Changes: monads of probability, measures, and valuations

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  1.  
    • CommentRowNumber1.
    • CommentAuthorPaoloPerrone
    • CommentTimeOct 11th 2019

    Created page, more to come.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorPaoloPerrone
    • CommentTimeOct 11th 2019

    Adding monads.

    There are many dead links for now - in the coming weeks, I will create all the relevant articles/sections.

    v1, current

    • CommentRowNumber3.
    • CommentAuthorPaoloPerrone
    • CommentTimeOct 20th 2019

    added short intro

    diff, v4, current

    • CommentRowNumber4.
    • CommentAuthorPaoloPerrone
    • CommentTimeJan 22nd 2020

    Added some details

    diff, v22, current

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 23rd 2020

    Just to note, Paolo, that you have to separate letters in Itex for it to render properly. I’ve just done this for dpd p in the integral in section 4.

    diff, v23, current

    • CommentRowNumber6.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 23rd 2020

    It’s good to have you constructing this page. At some point I want to get round to thinking about probability theory meets type theory. I was rambling out loud in a thread starting about here.

    • CommentRowNumber7.
    • CommentAuthorPaoloPerrone
    • CommentTimeJan 23rd 2020

    Thank you for the edit - yeah, I’m so used to LaTeX.

    About type theory and probability theory: it’s been a recurrent thought for me as well, but I don’t know enough about type theory to say something meaningful yet…

    • CommentRowNumber8.
    • CommentAuthorDavid_Corfield
    • CommentTimeJul 26th 2022

    Added

    • Ruben Van Belle, Probability monads as codensity monads. Theory and Applications of Categories 38 (2022), 811–842, (tac)

    diff, v32, current

  9. I noticed that in the overview table, the extra structure on PXPX for the Riesz and Baire monads was described as “the weak topology w.r.t continuous bounded functions”, which is unfortunately not quite correct (though it does hold on Polish spaces, where both reduce to the well-known monad further above in the table). I changed the description to “induced by cartesian closedness” which might be a bit vague, but I hope it’s sufficient for an overview like this.

    Benedikt Peterseim

    diff, v42, current

1 to 9 of 9

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