the ruling of state supreme courts are always the final judgment on a matter.
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In the Federal court system, the district courts are the "lowest" courts. Cases usually start in district court and are decided there. The circuit courts are courts of appeal. That means that you can appeal a district court's ruling to the circuit court (and then to the Supreme Court, if you still don't like the ruling). In that sense, the circuit courts are "higher" than the district courts.
The ruling of the court below the Supreme Court will be upheld. The Supreme Court is similar to an appeals court. If they don't want to take the case, then whatever the court ruling was will stand.
The U.S. Supreme Court upheld the ruling of the Illinois Supreme Court that considered the planned Skokie march by the National Socialist Party of America to be a matter of free speech. Thus, the National Socialist Party of America was allowed to march in Skokie and use the swastika as a symbol during their march. (Ultimately, no march was held in Skokie, rather in surrounding neighborhoods). Correction: Skokie case never reached the U.S. Supreme Court. It was considered the "easy case" because precedent from past 1st Amendment issues would have easily overturned the Illinois State Supreme Court ruling
majority opinion
the ruling of state supreme courts are always the final judgment on a matter.
what is the supreme courts ruling in the case Plessy vs ferguson
what is the supreme courts ruling in the case Plessy vs ferguson
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A United States Supreme Court decision is mandatory on all lower federal courts. That includes federal courts of appeal and federal district courts.
Supreme courts have full national jurisdiction, respecting the sovereignty of other nations in the process of ruling.
majority opinion
It was determined that minors are entitled to constitutional protections.