The phrase "asserted jurisdiction" is correct and usable in written English.
It can be used in legal contexts to indicate that a court or authority has claimed the right to make legal decisions over a particular case or matter.
Example: "The court asserted jurisdiction over the case, citing the defendant's significant connections to the state."
Alternatives: "claimed jurisdiction" or "exercised jurisdiction".
Ms. Spaulding said some countries had asserted jurisdiction over war crimes committed anywhere in the world.
The Secretary asserted jurisdiction in this Court by direct appeal under 28 U.S.C. 1252, 1253.
With its new bankruptcy law, China has asserted jurisdiction over who, in the last analysis, controls company assets.
To avert such pollution, Canada last week asserted jurisdiction over shipping within 100 miles of the Arctic archapelago.
In 1996, the Food and Drug Administration, after having expressly disavowed any such authority since its inception, asserted jurisdiction to regulate tobacco products.
For instance, after Kessler asserted jurisdiction over tobacco, Philip Morris and the other companies quickly filed their lawsuit to block him.
See, e. g., Academia San Jorge, 234 N.L.R.B. 1181 19788) (advisory opinion stating that Board would not assert jurisdiction over Catholic educational institution which did not meet jurisdictional standards); Windsor School, Inc., 199 N.L.R.B. 457, 200 N.L.R.B. 991 (1972) (declining jurisdiction where private, proprietary school did not meet jurisdictional amounts).
The general counsel, Robert E. Fabricant, issued a memorandum that said "E.P.A. cannot assert jurisdiction to regulate in this area".
In this case, we believe that Congress has clearly precluded the F.D.A. from asserting jurisdiction to regulate tobacco products.
Therefore, we will not decline to assert jurisdiction over these schools on such a basis". 223 N.L.R.B., at 1218.
Cf. Caulfield v. Hirsch, 95 LRRM 3164 (ED Pa.1977) (enjoining Board from asserting jurisdiction over elementary schools in Archdiocese of Philadelphia).
