#
On the Finite Dimensionality of Closed Subspaces in L_{p}(M, dμ) ∩ L_{q}(M, dν)

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

**Theorem**

**1.**

## 2. Finite Dimensionality of Closed Subspaces in ${L}_{p}\cap {L}_{q}$

**Theorem**

**2.**

**Lemma**

**1.**

**Proof.**

**Lemma**

**2.**

**Remark**

**1.**

**Proof.**

**Proof**

**of**

**Theorem**

**2.**

## 3. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Balinsky, A.A.; Prykarpatski, A.K.
On the Finite Dimensionality of Closed Subspaces in *L _{p}*(

*M*,

*dμ*) ∩

*L*(

_{q}*M*,

*dν*).

*Axioms*

**2021**,

*10*, 275. https://doi.org/10.3390/axioms10040275

**AMA Style**

Balinsky AA, Prykarpatski AK.
On the Finite Dimensionality of Closed Subspaces in *L _{p}*(

*M*,

*dμ*) ∩

*L*(

_{q}*M*,

*dν*).

*Axioms*. 2021; 10(4):275. https://doi.org/10.3390/axioms10040275

**Chicago/Turabian Style**

Balinsky, Alexander A., and Anatolij K. Prykarpatski.
2021. "On the Finite Dimensionality of Closed Subspaces in *L _{p}*(

*M*,

*dμ*) ∩

*L*(

_{q}*M*,

*dν*)"

*Axioms*10, no. 4: 275. https://doi.org/10.3390/axioms10040275