The phrase "assertions each" is not correct and does not convey a clear meaning in written English.
It seems to be an attempt to refer to individual assertions, but the phrasing is awkward and unclear.
Example: "The report included several assertions each requiring further evidence to support them."
Alternatives: "each assertion" or "individual assertions".
The decision to hear the case prompted confident assertions from each side that it was sure to prevail, and gave rise to calculations about the complicated political impact of possible rulings.
The twist, though, was that yesterday's arguments were something of a mirror image of the assertions by each side in the Republicans' federal lawsuit -- so far unsuccessful -- seeking an injunction to bar the recounts.
What Mr. Rove, the former political strategist for President Bush, actually said was that both Mr. McCain and Senator Barack Obama have "gone one step too far" in their assertions about each other.
Relevant examples included assertions that each assessment "provides an opportunity to correct misconceptions and actually learn/relearn concepts".
She and Codman argued that decorating should be considered a branch of architecture, "an assertion that each generation seems to discover anew".
Contrary to Thomas Merton's romantic assertion that each Shaker chair was made as though no other chair had been made before, Shaker chairs and other wooden objects were made in semi-industrial conditions for a growing middle-class market.
Prosecutors, in their argument for a single hearing, said they expected both men to make a much more central and common assertion: that each was less culpable and deserving of the death penalty than the higher-ups who ordered the bombings, starting with Mr. bin Laden.
AutoTutor provides a cycle of pump → hint → prompt → assertion for each expectation until the expectation is covered.
To what extent do film viewers' eye movements and measured film comprehension support either Spielberg's belief that he has absolute control over viewers' gaze and comprehension of a film, or contemporary film theories' and Tarantino's assertion that each viewer sees and understands a different film?
The MOCA show is organized in a loose, thematic manner that bunches artists together with associations of context and era - with the simple assertion that each of the artists has made a name for themselves in L.A. since the early 1970s.
