Note on Normal Decimals

@article{Davenport1952NoteON,  title={Note on Normal Decimals},  author={Harold Davenport and P{\'a}l Erd{\"o}s},  journal={Canadian Journal of Mathematics},  year={1952},  volume={4},  pages={58 - 63},  url={https://api.semanticscholar.org/CorpusID:14621341}}
A real number, expressed as a decimal, is said to be normal (in the scale of 10) if every combination of digits occurs in the decimal with the proper frequency. If a 1 a 2 … a k is any combination of k digits, and N(t) is the number of times this combination occurs among the first t digits, the condition is that 1 

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6 References

Note on normal numbers

was normal (in the sense of Borel) with respect to the base 10, a normal number being one whose digits exhibit a complete randomness. More precisely a number is normal provided each of the digits 0,

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