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Volume of critical points decreases under symmetric decreasing rearrangement

In the lecture note http://www.math.utoronto.ca/almut/rearrange.pdf, it was stated that the volume of the set of critical points decreases under symmetric decreasing rearrangement. It seems so obvious however I cannot prove it. There is also deleted topic in mathoverflow which stated exactly the same question as mine. Can someone help me? Thanks in advance!