Why does S. R. S. Varadhan uses $\Phi$ as symbol for $\emptyset$

Question

I've recently started studying some probability theory and looked through some books about this topic. In the first chapter of Probability Theory by S. R. S. VaradhanI encountered

Why is the empty set denoted as $\Phi$? I do only know the symbol $\emptyset$. Are there any historical reasons for using $\Phi$? I do not really like this.

Answer 1

This is the picture I took from the preview available at Google Books

The symbol is the standard one and I guess that your copy of the book has been obtained with poor OCR software.

I doubt that a book copyrighted in 2001 by the AMS is available as a free download.

Answer 2

My first thought was to suspect a typo, but he does seem to use this consistently. It's certainly not standard notation.

Answer 3

The empty set symbol $\varnothing$... I mean the empty set symbol $\emptyset$ is written quite similarly to the Greek letter $\phi$. And I have occasionally seen people use the capital version $\Phi$ instead, but it is rare.

FWIW, I could even imagine someone preferring $\Phi$ because it has very little chance of getting mixed up with zero; some people write zero as $\emptyset$ (to ensure that zero isn't confused with the letter $O$).

Answer 4

Well, here is a picture of the PDF version of the book at NYU, and there $\Phi$ is used as you can see.

The link to the PDF of the book is (see page 8)

Copy of Probability at NYU

My feeling is that a typist misread what Varadhan wrote by hand, and it remained in the book. Since Varadhan is such an authority, the notation $\Phi$ spread in some math circles. This is not the first time these kinds of things happen. Just think of the "common knowledge" that spinach has large iron content.