# A New Approach to the Lebesgue-Radon-Nikodym Theorem. with respect to Weighted p-adic Invariant Integral on ℤp

Rim, Seog-Hoon;Jeong, Joo-Hee

• Accepted : 2012.08.10
• Published : 2012.09.23
• 18 7

#### Abstract

We will give a new proof of the Lebesgue-Radon-Nikodym theorem with respect to weighted p-adic q-measure on $Z_p$, using Mahler expansion of continuous functions, studied by the authors in 2012. In the special case, q = 1, we can derive the same result as in Kim, 2012, Kim et al, 2011.

#### References

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#### Acknowledgement

Supported by : Kyungpook National University