The phrase "assertion about their" is correct and usable in written English.
It can be used when discussing a claim or statement made regarding a particular subject or group of people.
Example: "The researcher made an assertion about their findings, suggesting a new interpretation of the data."
Alternatives: "claim regarding their" or "statement about their".
We assume the assertion about is correct.
Horrible assertions about their bodies, their levels of intellect and personalities were read aloud.
Dr. Keim and her colleagues collected 101 samples from milk-sharing Web sites, recording the sellers' assertions about their own health and their methods of handling and storage.
Structure/function claims describe the effects of products on the body; however, manufacturers are not permitted to make assertions about their products' effects on specific diseases.
The spinmeisters of the art market, including fair promoters, are forever making assertions about their commercial conquests that have to be taken on blind faith.
Scientists outside India and Pakistan have questioned some of the two countries' assertions about their tests, and it was not immediately clear what size device Pakistan detonated today.
Effective guided-reading activities allow students to apply their background knowledge and experience to the "new". They provide students with means to revise predictions; search for tentative answers; gather, organize, analyze, and synthesize evidence; and begin to make assertions about their new understanding.
In order to get a fixed point, we need to prove for functions of B ¯ assertions about their transversality through barriers.
They also ask the Department of Justice to not interfere with state-legal programs and refute some of Sessions' assertions about their law.
A review of data on abortion notifications enabled us to validate farmers' assertions about their participation in the surveillance system.
