Mathematical Literature and Editions I have the following problem with some research papers I study, they mention papers/books with the wrong year or editions.
For example:

*

*KALLENBERG, O. (2006). Foundations of Modern Probability. Springer
Science & Business Media.

after some research I found that we have the versions:

*

*1st edition: © Springer Science+Business Media New York 1997


*2nd edition: © Springer-Verlag New York 2002


*3rd edition: © Springer Nature Switzerland AG 2021
Does anyone know, if there exists a database for mathematical literature, where I can easily check that references are valid even across different publishers?
 A: Free/Public Research Search Engines
There are quite a few free/public math research engines. However, the biggest one (and most notable) I have found is the zbMath|Open engine. It is a database where you can put in partial citations, or partial author names, and verify citations. For example, since I did not know KALLENBERG, O's first name, I put KALLENBERG, O* in the Authors tab like so:

Then their publications are listed on their user page like so:

Paid/College Account Research Search Engines
If you have access to a college account or are willing to go with a paid subscription, then AMS's MathSciNet is a database where you can put in partial citations, or partial author names, and verify citations like so:

and found all $94$ of their publications on their user profile. Then, I just use the "Search within results" to find the same results you found (I scrubbed out my local library's name for privacy reasons):

In addition, there is CAS Solution's SciFinder and Wiley's Wiley Online Library - both of which are accessible with paid subscriptions or a college account.
Overall
Each one was able to inform which publisher/journal each publication came from, and could show which edition each one was. Thus, you just need to know at few critical pieces of information (author name, title, etc.) and the engines should be able to find the rest. This is how you'd be able to double check if a citation is valid, because if one thing is wrong, but a couple of others are correct, then you should be able to find something.
