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MMLU-Pro / 8614 / Suppose H is a Banach space, and x_n…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Suppose H is a Banach space, and {x_n}\in H, x\in H. Then x_n weakly converges to x is equivalent to: ||x_n|| is bounded; for a dense set M* in H*, it holds \lim_{n\rightarrow\infty} f(x_n)=f(x) for all f\in M*. Is this correct? Answer 1 for yes and 0 for no.

category

math

options

  1. -2.0
  2. 3.0
  3. 1.5
  4. -0.5
  5. -1.0
  6. 0.5
  7. 0.0
  8. 1.0
  9. 2.0
  10. 2.5

src

theoremQA-Math

Discussion

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Source and history

upstream_id / Original problem ID
8614
task_id
9fcca07a-5858-5be8-9264-a79ba8b5e7c5
task_key
default--test--8614
task_revision_id
1
config / split
default / test

Official source

initial import