Final answer:
The appeal trial for a woman in Los Angeles, California convicted of murder would first take place in the California appellate court, and if further appealed, could go to the California Supreme Court and potentially the U.S. Supreme Court.
Step-by-step explanation:
If a woman in Los Angeles, California is convicted of murder and is sentenced to death, but then appeals her conviction claiming innocence, the next step in the legal process would be for her appeal to be heard in the California appellate court. If the appeal is not in her favor there and further appeal is sought, the case may then go to the California Supreme Court. Should the case raise substantial federal questions or issues of constitutional law after exhausting state court appeals, it could potentially be considered by the U.S. Supreme Court upon granting a writ of certiorari. It's important to understand this hierarchy: from trial courts, where cases are first heard; to appellate courts, which review decisions made by trial courts; then possibly the state's highest court; and finally, in some cases, the U.S. Supreme Court.