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  "body": "\n## Summary\n\nTake a family of [[probability measures|059TJN0NZ1]].\nIts infinite product measure is the probability measure on the product space under which the coordinates are independent with the given laws.\nIt is defined on the [[product σ-algebra|6HVCTJGB61]] and is determined by its values on cylinder sets.\nIt exists for every family of probability spaces, with an arbitrary index set.\nIt is the model for infinite sequences of independent trials, such as repeated coin tossing.\n\n## Explanations\n\n### L1 human\n\nImagine tossing a fair coin forever.\nAn outcome is an infinite sequence of heads and tails.\nThe infinite product measure says how likely a set of such sequences is: for example, the sequences that start with heads, tails, heads have probability $\\tfrac18$.\nOnly probability measures are used, because a product of infinitely many total masses must make sense, and $1 \\cdot 1 \\cdot 1 \\cdots = 1$.\n",
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