I'm wondering where the relative probabilistic distance was first studied: $$d(A,B) =\mathbb P(\overline A\cup\overline B\mid A\cup B)$$ where $\overline A$ is the complement of $A$.

A web search turned up this:

@TechReport{Yianilos91,
  author =   "Peter N. Yianilos",
  title =    "Normalized Forms for Two Common Metrics",
  institution =  "NEC Research Institute",
  year =     {1991,2002}
}

which contains a detailed proof that $d $ obeys the triangle inequality, but surely that was discovered prior to 1991?

Update: On a seemingly related note, Cathy O'Neil mentions at 5:00 in Deciphering recommendation engines, http://youtu.be/lzavwJy1SgQ that $$\mathbb P(A\mid A\cup B)$$ is a mathematically interesting notion of closeness.

I'm wondering where the relative probabilistic distance or Jaccard distance was first studied: $$d(A,B) =\mathbb P(\overline A\cup\overline B\mid A\cup B)$$ where $\overline A$ is the complement of $A$.

A web search turned up this:

@TechReport{Yianilos91,
  author =   "Peter N. Yianilos",
  title =    "Normalized Forms for Two Common Metrics",
  institution =  "NEC Research Institute",
  year =     {1991,2002}
}

which contains a detailed proof that $d $ obeys the triangle inequality, but surely that was discovered prior to 1991?

On a seemingly related note, Cathy O'Neil mentions at 5:00 in Deciphering recommendation engines, http://youtu.be/lzavwJy1SgQ that $$\mathbb P(A\mid A\cup B)$$ is a mathematically interesting notion of closeness.

I'm wondering where the relative probabilistic distance was first studied: $$d(A,B) =\mathbb P(\overline A\cup\overline B\mid A\cup B)$$ where $\overline A$ is the complement of $A$.

A web search turned up this:

@TechReport{Yianilos91,
  author =   "Peter N. Yianilos",
  title =    "Normalized Forms for Two Common Metrics",
  institution =  "NEC Research Institute",
  year =     {1991,2002}
}

which contains a detailed proof, but surely this was discovered prior to 1991?

I'm wondering where the relative probabilistic distance was first studied: $$d(A,B) =\mathbb P(\overline A\cup\overline B\mid A\cup B)$$ where $\overline A$ is the complement of $A$.

A web search turned up this:

@TechReport{Yianilos91,
  author =   "Peter N. Yianilos",
  title =    "Normalized Forms for Two Common Metrics",
  institution =  "NEC Research Institute",
  year =     {1991,2002}
}

which contains a detailed proof that $d $ obeys the triangle inequality, but surely that was discovered prior to 1991?

Update: On a seemingly related note, Cathy O'Neil mentions at 5:00 in Deciphering recommendation engines, http://youtu.be/lzavwJy1SgQ that $$\mathbb P(A\mid A\cup B)$$ is a mathematically interesting notion of closeness.

I'm wondering where the relative probabilistic distance was first studied: $$d(A,B) =\mathbb P(\overline A\cup\overline B\mid A\cup B)$$ where $\overline A$ is the complement of $A$.

A web search turned up this:

Goodman, I. R. and Kramer, G. F. (1996), Extension of relational event algebra to a general decision making setting, Proceedings of the Conference on Intelligent Systems: A Semiotic Perspective, National Institute of Standards and Technology.

where $d$ is called $\mathbf r_{\mathbb P}$, but surely that's not the first occurrence?

I'm wondering where the relative probabilistic distance was first studied: $$d(A,B) =\mathbb P(\overline A\cup\overline B\mid A\cup B)$$ where $\overline A$ is the complement of $A$.

A web search turned up this:

@TechReport{Yianilos91,
  author =   "Peter N. Yianilos",
  title =    "Normalized Forms for Two Common Metrics",
  institution =  "NEC Research Institute",
  year =     {1991,2002}
}

which contains a detailed proof, but surely this was discovered prior to 1991?