TY - JOUR AU - Roope Anttila PY - 2020/11/04 Y2 - 2024/03/28 TI - Local Entropy and Lq-Dimensions of Measures in Doubling Metric Spaces JF - The PUMP Journal of Undergraduate Research JA - PUMP J. Undergrad. Res. VL - 3 IS - 0 SE - Articles DO - 10.46787/pump.v3i0.2434 UR - https://journals.calstate.edu/pump/article/view/2434 AB - We define restricted entropy and Lq-dimensions of measures in doubling metric spaces and show that these definitions are consistent with the monotonicity of Lq-dimensions. This provides a correct proof for a theorem considering the relationships between local entropy and Lq-dimensions in a paper by Käenmäki, Rajala and Suomala, the original proof of which makes use of a slightly erroneous proposition. ER -