设[tex=0.786x1.286]YggwMQ4w3PxfhkmL0NfgdQ==[/tex]为[tex=1.357x1.071]xK5z3G1XXIQX+IF4DKX5dQ==[/tex]中任一子集，[tex=0.571x1.286]mRKL/orzOudCEARA8qn3Kw==[/tex]为给定正数，对于任何[tex=2.286x1.286]agbj3VZO5e3/0KnI5wCMSKLl3aP3w8IOLV//cMDwSdM=[/tex]，令[tex=4.429x1.286]BESAJyFee+P3k2ruVPVrF0S+pQXrYYfXdi68VaO99fo=[/tex][tex=5.929x2.143]0S/Yo0LjwOeqDaAs67k1mDlhf231PFkPhzqe9kSqPdDy6Pn+ZJZgJK+SMZzqs731[/tex]，其中[tex=2.571x1.286]CG3XklyU1r5lYsDIJZE9feAbmQ74fxAdzZDuuYGbFKQ=[/tex]表示[tex=1.214x1.286]G7PAvUeEdHzh0i+xlrGNCg==[/tex]的直径，且下确界对一切满足[tex=3.929x1.286]z5VoLK6Fr0+lWCbhtAQTiOX/pZnJs23N68p4lXZqRnk=[/tex]而[tex=4.357x1.286]CG3XklyU1r5lYsDIJZE9fc+Vah68H5turckMLuOx1DWPtjhMXb4jCngKhtmMmGZP[/tex][tex=5.5x1.286]AunXBj/S27oeaN9whASfB2b4id2SvntOVhM1hHejXzM=[/tex]的集列[tex=2.143x1.286]b6waMT6MEWtqDu3wjq4WQw==[/tex]而取。再令[tex=15.714x1.786]KoeL7XruSMgiRqTcEJMpp0PJqf2jz71FyMe3NmAT7fTUq99SoRwSU9epXyYDrqzFNeCNKN9RHYwZiI8StTb/d7bPPjQ6Jwo79QKb0HH8BE7TdD1etQuGq4kAl/ccS0sfl/K/U6i8SsUGASapjJfiCt7lVji91PFg4ciiXFX5nog=[/tex]，试证[tex=1.357x1.286]dMhmAjJDltdnhtHC532AoA==[/tex]为基本集[tex=1.357x1.071]xK5z3G1XXIQX+IF4DKX5dQ==[/tex]上的外测度，并满足条件：若[tex=5.143x1.286]MCSTiw/Lu/L2iN1YcmXl9R8tSjo3pw6CfICOf3JdPog=[/tex]，则当[tex=2.571x1.286]1Tg1GTXi7+oO2cljOmkx0s4NSmFnKZ8+wvPBngowTu4=[/tex]时，[tex=4.643x1.286]Df2bPBp4hcoXg/DvrxVTFSRuXrihHkf5pBEl6ZnACys=[/tex]（[tex=1.357x1.286]dMhmAjJDltdnhtHC532AoA==[/tex]称为豪斯多夫（F.Hausdorff）测度）。