The phrase "establish the notion" is correct and usable in written English.
You can use it when you are referring to the idea or concept of something. For example, "The research paper sought to establish the notion that technology can be beneficial to society."
Entebbe had helped establish the notion that Israel's reach was simply too long for it to be defeated militarily.
As newsprint becomes a smaller part of the business, "you want to establish the notion that it's worth something online," Mr. Brill said.
Centuries before modern preservation laws, it was military jurists like Emmerich de Vattel who helped establish the notion that governments at war had a legal duty to protect heritage including that of their conquered enemies.
This work was primarily an attempt to establish the notion of duration, or lived time, as opposed to what Bergson viewed as the spatialized conception of time, measured by a clock, that is employed by science.
His and his friends' devotion to a quartet of filmmakers Otto Preminger, Raoul Walsh, Fritz Lang, and Joseph Losey did much to establish the notion of mise en scène (what, in theatre, would be called direction or staging) as a fundamental concept of film criticism and a strange aspiration for (at least some) young filmmakers.
His and his friends' devotion to a quartet of filmmakers — Otto Preminger, Raoul Walsh, Fritz Lang, and Joseph Losey — did much to establish the notion of mise en scène (what, in theatre, would be called direction or staging) as a fundamental concept of film criticism and a strange aspiration for (at least some) young filmmakers.
He must first re-establish the notion that if you work hard and play by the rules in America you will get ahead in life.
Also in 1971, the U.S. Supreme Court established the notion of "disparate impact" — the predominant legal theory used to review unintended discrimination.
The civil rights movement firmly established the notion of bias as unconscious prejudice, to the point where the protestation "I'm not biased" came to sound suspect.
Welles established the notion of the epochal first feature that didn't just launch a career but knocked the history of cinema into a new orbit.
